ModelMicrobiome is a novel platform for testing the performance and assumptions underlying ecological inference of microbiomes. Whereas previous benchmarking and modeling efforts have used case-control frameworks, and/or used randomized real data, none have tested the accuracy of ecological inference following a sequence count normalization procedure. Previous efforts have focused on the ability to accurately detect a change in relative abudance (i.e. differential abundance analysis). But these tests do not reflect how well the ecological relationships are preserved through the normalization process (e.g. relationship between the taxa and their environment or among taxa). This software does not attempt to address bias that is introduced by the sequencing, DNA purification, or field sampling efforts. It only is meant as a tool to better understand the effect that any post-hoc sequence count normalization has on our ability to infer underlying ecological relationships.
To further clarify the limits of this software, it is not intended to be applied to metagenomics analyses that derive from shotgun sequence data. There are database and sequencing biases that are particular to whole genome sequencing that must be addressed separately and that may confound the inferences made from this software. THIS SOFTWARE IS NOT DESIGNED TO ADDRESS SHOTGUN SEQUENCING OR ION TORRENT ETC. SEQUENCING. This software is designed specifically for amplicon (i.e. metabarcoding) studies of a single gene locus used to infer population structure. For more detailed information about how the indexes are constructed, refer to (DOI: … )
This software was written under R version 3.6.1. R version 4 has been published with major updates to some of the core mechanics. Model.MicrobiomeV2 will be updated for R 4.0 soon.
This tutorial will address the primary functionalities of Model.Microbiome, and provide an example of how it can be used in the course of an experimental workflow.
First, let’s install Model.Microbiome:
# update anything from my local computer (for me as I work, not you...) ####
#setwd("/Users/maullabmacbookpro/Documents/GitHub/Model.Microbiome")
#library(devtools)
#library(roxygen2)
#document()
#now install ####
devtools::install_github("djeppschmidt/Model.Microbiome")
## Skipping install of 'Model.Microbiome' from a github remote, the SHA1 (775db361) has not changed since last install.
## Use `force = TRUE` to force installation
Now load all the other packages we need (or download and load if you haven’t already):
# load required packages ####
library(Model.Microbiome)
library(reshape2)
library(ggplot2)
library(vegan)
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library(dplyr)
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library(plyr)
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library(phyloseq)
library(viridis)
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library(ranacapa)
library(edgeR)
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library(car)
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The core functionality of Model.Microbiome is to create a model microbial community, then simulate sequencing by subsampling from it. This simulated count data can then be normalized using any normalization method. This is handled by the run.analysis2() function. I recommend running this function with SuppressWarnings(). It is normal for the linear model functions that Model.Microbiome references to give warnings whenever the fit is perfect; these warnings stack up across the simulation and become overwhelming.
Building the model community works sequenially by: 1. creating an environment made out of 5 environmental parameters, 30 sites, and 6 statistically distinctive “experimental” conditions. a. environmetnal paramters 1-3 change in mean and variance according to the experimental condition. b. environmental parameters 4 and 5 are unrelated to the experimental design, but do affect taxon abundance c. the sampling environment consists of 30 samples, divided into 6 experimental conditions/treatment (or 5 reps per condition) d. the environmental parameters have the same mean and variance within each condition/treatment every time the software is run; however, the values of any given run are randomly drawn from this distribution. Therefore no two runs will have exactly the same environment, but they will represent exactly the same experiment.
NOTE: SEE SECTION DETAILS FOR CAVEATS ABOUT THIS SELECTION PROCESS!!
NOTE: While Model.Microbiome does construct networks and taxon associations in downstream analyses, it does not model those relationships explicitly; no species function refers explicitly to another species.
So let’s look at the function. It has several inputs necessary:
commonN: Number of taxa that have a global distribution groupN: Number of taxa that are group-specific singleN: Number of taxa that are sample-specific
NOTE: there are 700 species functions that the software selects from. For each of these values, it uses a random selection routine. It includes resampling among the groups. This means that:
THERE IS A CHANCE THAT A TAXON MAY END UP REPRESENTING SEVERAL GROUPS, OR SAMPLES.
D: mean sampling depth (i.e. simulating sequencing) V: variance of sampling depth.
method: names of the functions to be used for count normalization (see below for details)
Let’s look at an example using a narmalization method included with Model.Microbiome.This implementation creates a single output object that contains the phyloseq objects created before, and a number of different statistics. In order to get it to work, we need at least one methods function:
method<-c("QSeq")
model<-suppressWarnings(run.analysis2(commonN=30, groupN=20, singleN=5, D=500, V=250, method))
Note that rarefaction curves are generated automatically for the reference condition in each simulation run. This helps us judge whether our subsampling level is under sampling in general. It also allows us to examine the diversity of each samople; we can see that there are distinctions in diversity among the experimental conditions.
The QSeq method is a native Model.Microbiome method, but let’s look at how it was constructed to give a framework for how the user can create functions that work with Model.Microbiome:
# these functions are already provided as a part of Model.Microbiome
make.scaled2<-function(ps, val, scale){
scaled<-data.frame(mapply(`*`, data.frame(as.matrix(otu_table(transform_sample_counts(ps, function(x) x/sum(x))))), scale * val))# sample_data(ps)$val))
names<-rownames(data.frame(as.matrix(otu_table(ps))))
rownames(scaled)<-names
scaled<-round(scaled)
p2<-ps
otu_table(p2)<- otu_table(scaled, taxa_are_rows=T)
p2
}
QSeq<-function(ps){
scale<-sample_data(ps)$DensityF
out<-make.scaled2(ps, val=2*mean(sample_sums(ps)), scale)
out
}
Notice that this is actually one function nested within another. The wrapper helps the function to play nice. It’s easy to replicate wrappers to provide the underlying function with different inputs if we want to test the different potential conditions. For example, our QSeq function is meant to replicate the normalization technique called quantitative sequencing. This technique combines quantitative data from QPCR with sequence count distributions to normalize the sequence counts in each sample by the relative total sequence counts of that sample compared to other samples. This should more closely approximate the behavior of the sampled community than relative abundance. To do this though, we need to decide what the mean value for the sample-wise abundance normalization. We could make several versions of the QSeq function to test what is the optimal mean sample-wise total abundance. To do this we change the value parameter as follows:
QSeq0.5<-function(ps){
scale<-sample_data(ps)$DensityF
out<-make.scaled2(ps, val=0.5*mean(sample_sums(ps)), scale)
out
}
QSeq1<-function(ps){
scale<-sample_data(ps)$DensityF
out<-make.scaled2(ps, val=mean(sample_sums(ps)), scale)
out
}
QSeq2<-function(ps){
scale<-sample_data(ps)$DensityF
out<-make.scaled2(ps, val=2*mean(sample_sums(ps)), scale)
out
}
QSeq3<-function(ps){
scale<-sample_data(ps)$DensityF
out<-make.scaled2(ps, val=3*mean(sample_sums(ps)), scale)
out
}
QSeq10<-function(ps){
scale<-sample_data(ps)$DensityF
out<-make.scaled2(ps, val=10*mean(sample_sums(ps)), scale)
out
}
QSeq100<-function(ps){
scale<-sample_data(ps)$DensityF
out<-make.scaled2(ps, val=100*mean(sample_sums(ps)), scale)
out
}
In this way we end up with a number of different functions that can be called independently, but that work on the same underlying mechanic. This is important if we have a method that we want to optimize in some way.
If we want to use all of our methods in our simulation study, then we simply do:
method<-c("QSeq0.5", "QSeq1", "QSeq2", "QSeq3", "QSeq10", "QSeq100")
Then we implement it in the analysis pipeline:
model<-suppressWarnings(run.analysis2(commonN=30, groupN=20, singleN=5, D=500, V=250, method))
We can call the phyloseq object from any one of the normalization (including the reference data and the raw sequence counts):
model$model$comm
model$raw$comm
model$QSeq0.5$comm
model$QSeq1$comm
model$QSeq2$comm
model$QSeq3$comm
model$QSeq10$comm
Model.Microbiome also automatically calculates several metrics. For example, it calculates automatically an experiment-wide PERMANOVA for each method and each factor. So for example if we look at the reference, we have a seperate permanova for the experimental category:
model$model$PERMANOVA$Category
##
## Call:
## adonis(formula = x ~ Factor2, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Factor2 5 5.7833 1.15665 47.094 0.9075 0.001 ***
## Residuals 24 0.5895 0.02456 0.0925
## Total 29 6.3727 1.0000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
And each of the environmental factors:
model$model$PERMANOVA$F1
##
## Call:
## adonis(formula = x ~ F1, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F1 1 1.1235 1.12347 5.9927 0.17629 0.001 ***
## Residuals 28 5.2492 0.18747 0.82371
## Total 29 6.3727 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$model$PERMANOVA$F2
##
## Call:
## adonis(formula = x ~ F2, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F2 1 0.8850 0.88502 4.5156 0.13888 0.003 **
## Residuals 28 5.4877 0.19599 0.86112
## Total 29 6.3727 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$model$PERMANOVA$F3
##
## Call:
## adonis(formula = x ~ F3, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F3 1 1.7116 1.71160 10.282 0.26858 0.001 ***
## Residuals 28 4.6611 0.16647 0.73142
## Total 29 6.3727 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$model$PERMANOVA$F4
##
## Call:
## adonis(formula = x ~ F4, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F4 1 0.4034 0.40338 1.8921 0.0633 0.076 .
## Residuals 28 5.9693 0.21319 0.9367
## Total 29 6.3727 1.0000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$model$PERMANOVA$F5
##
## Call:
## adonis(formula = x ~ F5, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F5 1 0.4381 0.43805 2.0667 0.06874 0.063 .
## Residuals 28 5.9347 0.21195 0.93126
## Total 29 6.3727 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
We can compare any of these across treatments:
model$model$PERMANOVA$F1 # reference condition!
##
## Call:
## adonis(formula = x ~ F1, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F1 1 1.1235 1.12347 5.9927 0.17629 0.001 ***
## Residuals 28 5.2492 0.18747 0.82371
## Total 29 6.3727 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$raw$PERMANOVA$F1 # not normalized
##
## Call:
## adonis(formula = x ~ F1, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F1 1 1.0582 1.05818 4.2325 0.13131 0.001 ***
## Residuals 28 7.0003 0.25001 0.86869
## Total 29 8.0585 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$QSeq0.5$PERMANOVA$F1 # lowest mean value
##
## Call:
## adonis(formula = x ~ F1, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F1 1 1.1141 1.11410 5.7043 0.16925 0.001 ***
## Residuals 28 5.4687 0.19531 0.83075
## Total 29 6.5828 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$QSeq1$PERMANOVA$F1 #...
##
## Call:
## adonis(formula = x ~ F1, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F1 1 1.1125 1.11252 5.7102 0.16939 0.001 ***
## Residuals 28 5.4552 0.19483 0.83061
## Total 29 6.5678 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$QSeq2$PERMANOVA$F1 #...
##
## Call:
## adonis(formula = x ~ F1, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F1 1 1.1122 1.11218 5.708 0.16934 0.001 ***
## Residuals 28 5.4557 0.19485 0.83066
## Total 29 6.5678 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$QSeq3$PERMANOVA$F1 #...
##
## Call:
## adonis(formula = x ~ F1, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F1 1 1.1126 1.11256 5.7076 0.16933 0.001 ***
## Residuals 28 5.4580 0.19493 0.83067
## Total 29 6.5705 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$QSeq10$PERMANOVA$F1
##
## Call:
## adonis(formula = x ~ F1, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F1 1 1.1120 1.11198 5.7058 0.16928 0.001 ***
## Residuals 28 5.4568 0.19489 0.83072
## Total 29 6.5688 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$QSeq100$PERMANOVA$F1# highest mean value
##
## Call:
## adonis(formula = x ~ F1, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F1 1 1.1120 1.11202 5.7062 0.16929 0.001 ***
## Residuals 28 5.4567 0.19488 0.83071
## Total 29 6.5687 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
You’ll notice that the QSeq PERMANOVA tables are very similar to the reference PERMANOVA table, and that the un-normalized table is a bit different. This is great! It tells us that we are recapturing some lost information from the subsampling.
Model.Microbiome uses a few metrics to understand bias that is introduced through the normalization process. All the metrics in Model.Microbiome consist of the ouput from an analysis conducted on a normalized dataset (treatment) divided by the same analysis conducted on the reference community. For example, if we are interested in the relationship between a taxon an the environment, we could construct a linear model where abundance of taxon x depends on environment A. The R-squared of this model would represent the amount of information captured by the model. If we applied this model to both the reference community, and the normalized community, then we have a measure of the “actual” relationship and the inferred relationship after our normalization, respectively. The ratio of these values gives us a comparable value where 1 represents a perfect match; greater than 1 indicates the normalization method leads to overestimating the explanatory power of the environmental factors on the abundance of the taxon; and a value of less than one indicates that the normalization underestimates the explanatory value of the environmental parameter. All of the indices are based on this interpretation principle.
Here is a brief description of each index:
Loss of information index (LII) is based on a linear model approach, but instead of regressing the taxa against the environment and comparing the outputs, it regresses the treatment (normalized data) against the reference (pre-sampling). Thus the R-squared value of the model is a direct measure of how well reference abundance predicts the normalized abundance. The LII output has several components;
$Index : index value which is the sum from all taxa of (1 - the linear regression r-squared values) divided by the total number of taxa. This is a single value for the whole run. Lower scores equate to less overall information lost. The LII can be interrpeted as “mean information lost per taxon”
$R : a named list of the R squared values that are summed in the Index, one per taxon in the run.
$diff : a list of (1 - the r-squared values) for the Index value, one for each taxon. This is useful to identify which taxa are deviating substantially, and help with troubleshooting the normalization method, and identifying why any patterns might exist.
All of these can be accessed from the output object (see output object map).
The second set of metrics consist of linear regressions of the taxa (or whole community) against environmental and experimental design predictors. This test allows us to diagnose the effect that our normalization protocol has on our ability to infer relationships between the taxa and the environment / experimental condition. The primary outputs of this process are then taken as a ratio to the reference for interpretation.
$lmRatiotab : list of taxa and their R-squared values between taxon and the environment, normalized by the reference
$lmRatiotab.model : list of taxa and their R-squared values between taxon and the experimental design, normalized by the reference
lmRatiotab or lmRatiotabl.model values that are close to 1 represent near perfect retention of the ecological relationship. Values that approach 0 or are above 1.5 represent substantial loss of accuracy. There should be no negative values.
There are also metrics that reflect beta diversity. The R-Squared value for a PERMANOVA analysis of the experimental conditions, and environmental parameters against a Bray-Curtis transformed count table are used to calculate a R-Ration between the reference community and the treatment communities. Also, modularity is calculated based on a correlation matrix using a number of different construction methods. These methods will be addressed in more detail later.
#Object Map:
Output Object Map
The speciesMeta object stores a few taxon-specific metrics that help us interpret the outcomes;
$prevalence is a taxon-wise measure of how many sites the taxon actually occures in (in the reference community).
$mean_abundance is a taxon-wise measure of the mean abundance of each taxon across all sites (in the reference community)
$sd_abundance is a taxon-wise measure of the standard deviation in abundance of each taxon across all sites (again, reference community).
$M.Eval is the mean of the relative abundance of the taxon at each site divided by the sampling depth of that site. This is meant to represent an unweigthed estimation of the likelihood that a taxon will be sampled at any site, given that they exist in that site. Lower values mean the taxon is generally less abundant, and less likely to be sampled in any of the sites.
These taxon-specific data can be useful for exploring patterns when it’s time to interpret an experimental run. Let’s look at some example plots that demonstrate the utility of these metadata:
First, let’s examine the relationship between the expected likelihood of sampling a taxon and the amount of information that is lost. In this plot, the method (QSeq0.5) axis represents 1-(r-squared of treatment vs reference) abundance values for each taxon in the community. Thus higher values equate to more information lost:
ggplot(model$model$SpeciesMeta, aes(x=log10(M.Eval),y=log(QSeq0.5), col=prevalence))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
The color represents the prevalence, we can see that in this case, there are many taxa that lose no information (along the bottom of the graph). Most of these are taxa that only occur in one sample. Let’s color the samples differently:
ggplot(model$model$SpeciesMeta, aes(x=M.Eval,y=QSeq0.5, col=log(mean_abundance)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
ggplot(model$model$SpeciesMeta, aes(x=log(M.Eval),y=log(QSeq0.5), col=log(mean_abundance)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
We can see that taxa with high mean values are much more likely to retain their information through the sampling.
ggplot(model$model$SpeciesMeta, aes(x=log10(M.Eval),y=log(QSeq0.5), col=log(mean_abundance)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
ggplot(model$model$SpeciesMeta, aes(x=log10(M.Eval),y=log(QSeq1), col=log(mean_abundance)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
ggplot(model$model$SpeciesMeta, aes(x=log10(M.Eval),y=log(QSeq10), col=log(mean_abundance)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
ggplot(model$model$SpeciesMeta, aes(x=log10(M.Eval),y=log(QSeq100), col=log(mean_abundance)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
We can see that in particular there is a shift in the amount of information that is lost in the middle M.Eval ranges; at high E.Val, there is relatively less information lost and so the values are more stable. At the low end, the lost information effects are dominated by whether or not the taxa happen to be detected; in the middle, taxa are regularly detected but their abundance is very dependent on sampling depth of the sample. Thus this is the area where we regain the most information.
ggplot(model$model$SpeciesMeta, aes(x=prevalence,y=QSeq0.5, col=log(mean_abundance)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
ggplot(model$model$SpeciesMeta, aes(x=prevalence,y=QSeq1, col=log(mean_abundance)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
ggplot(model$model$SpeciesMeta, aes(x=prevalence,y=QSeq10, col=log(mean_abundance)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
ggplot(model$model$SpeciesMeta, aes(x=prevalence,y=QSeq100, col=log(mean_abundance)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
ggplot(model$model$SpeciesMeta, aes(x=log(mean_abundance),y=QSeq0.5, col=log(prevalence)))+
geom_point()+
scale_color_viridis_c(option="C")+
theme_classic()
We can see that taxa that have higher prevalence also tend to retain more information; the one caveat is the taxa that exist in only one site. As long as they are detected, they retain perfect information.
We can explore to see how well species abundance and prevalence explain the LII:
summary(lm(model$model$SpeciesMeta$QSeq0.5~model$model$SpeciesMeta$prevalence*log(model$model$SpeciesMeta$mean_abundance)))
##
## Call:
## lm(formula = model$model$SpeciesMeta$QSeq0.5 ~ model$model$SpeciesMeta$prevalence *
## log(model$model$SpeciesMeta$mean_abundance))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.50230 -0.21672 -0.05508 0.15703 0.72949
##
## Coefficients:
## Estimate
## (Intercept) -0.467800
## model$model$SpeciesMeta$prevalence -0.004668
## log(model$model$SpeciesMeta$mean_abundance) -0.085972
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) -0.005053
## Std. Error
## (Intercept) 0.136438
## model$model$SpeciesMeta$prevalence 0.010661
## log(model$model$SpeciesMeta$mean_abundance) 0.017884
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) 0.001797
## t value
## (Intercept) -3.429
## model$model$SpeciesMeta$prevalence -0.438
## log(model$model$SpeciesMeta$mean_abundance) -4.807
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) -2.812
## Pr(>|t|)
## (Intercept) 0.000824
## model$model$SpeciesMeta$prevalence 0.662241
## log(model$model$SpeciesMeta$mean_abundance) 4.34e-06
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) 0.005729
##
## (Intercept) ***
## model$model$SpeciesMeta$prevalence
## log(model$model$SpeciesMeta$mean_abundance) ***
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2905 on 124 degrees of freedom
## Multiple R-squared: 0.3896, Adjusted R-squared: 0.3748
## F-statistic: 26.38 on 3 and 124 DF, p-value: 2.889e-13
# look at prediction of prevalence
summary(lm(model$model$SpeciesMeta$QSeq0.5~model$model$SpeciesMeta$prevalence*log(model$model$SpeciesMeta$mean_abundance)))
##
## Call:
## lm(formula = model$model$SpeciesMeta$QSeq0.5 ~ model$model$SpeciesMeta$prevalence *
## log(model$model$SpeciesMeta$mean_abundance))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.50230 -0.21672 -0.05508 0.15703 0.72949
##
## Coefficients:
## Estimate
## (Intercept) -0.467800
## model$model$SpeciesMeta$prevalence -0.004668
## log(model$model$SpeciesMeta$mean_abundance) -0.085972
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) -0.005053
## Std. Error
## (Intercept) 0.136438
## model$model$SpeciesMeta$prevalence 0.010661
## log(model$model$SpeciesMeta$mean_abundance) 0.017884
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) 0.001797
## t value
## (Intercept) -3.429
## model$model$SpeciesMeta$prevalence -0.438
## log(model$model$SpeciesMeta$mean_abundance) -4.807
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) -2.812
## Pr(>|t|)
## (Intercept) 0.000824
## model$model$SpeciesMeta$prevalence 0.662241
## log(model$model$SpeciesMeta$mean_abundance) 4.34e-06
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) 0.005729
##
## (Intercept) ***
## model$model$SpeciesMeta$prevalence
## log(model$model$SpeciesMeta$mean_abundance) ***
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2905 on 124 degrees of freedom
## Multiple R-squared: 0.3896, Adjusted R-squared: 0.3748
## F-statistic: 26.38 on 3 and 124 DF, p-value: 2.889e-13
summary(lm(model$model$SpeciesMeta$QSeq100~model$model$SpeciesMeta$prevalence*log(model$model$SpeciesMeta$mean_abundance)))
##
## Call:
## lm(formula = model$model$SpeciesMeta$QSeq100 ~ model$model$SpeciesMeta$prevalence *
## log(model$model$SpeciesMeta$mean_abundance))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.51005 -0.13549 -0.06243 0.09806 0.73822
##
## Coefficients:
## Estimate
## (Intercept) -0.141802
## model$model$SpeciesMeta$prevalence -0.019523
## log(model$model$SpeciesMeta$mean_abundance) -0.028830
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) -0.007697
## Std. Error
## (Intercept) 0.105990
## model$model$SpeciesMeta$prevalence 0.008281
## log(model$model$SpeciesMeta$mean_abundance) 0.013893
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) 0.001396
## t value
## (Intercept) -1.338
## model$model$SpeciesMeta$prevalence -2.357
## log(model$model$SpeciesMeta$mean_abundance) -2.075
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) -5.513
## Pr(>|t|)
## (Intercept) 0.183
## model$model$SpeciesMeta$prevalence 0.020
## log(model$model$SpeciesMeta$mean_abundance) 0.040
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) 1.95e-07
##
## (Intercept)
## model$model$SpeciesMeta$prevalence *
## log(model$model$SpeciesMeta$mean_abundance) *
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2257 on 124 degrees of freedom
## Multiple R-squared: 0.462, Adjusted R-squared: 0.449
## F-statistic: 35.5 on 3 and 124 DF, p-value: < 2.2e-16
Pay close attention to the R-squared values of the model. We can see that the prevalence and mean abundance explain the highest amount of variance in the LII model. This doesn’t necessarily mean that this model performs better; imagine if the relative patterns of all taxa are perfectly preserved, then there would be no relationship between the mean abundance, prevalence and information that is lost through sampling. Conversely, if we have a really high predictive power between the abundance, prevalence, and lost information, it doesn’t necessarily mean that the normalization is creating more bias in the dataset as there are likely real effects of relative abundance on the likelihood of detection in subsampling. This is to say that the statistics and the plots should be examined within the context of how the normalization procedure is known to operate in order to determine if it is creating bias. In this instance, QSeq0.5 decreases the R-squared of the model because some taxa are rounded down to 0, creating an anomaly that is removed at QSeq10 and QSeq100.
A note about lmRatio and lmRatio.model: As a reminder, the lmRatio and lmRatio.model values are the ratio of r-squared values of a model using normalized versus reference count tables. lmRatio is a model that regresses taxa against the environmental variables; lmRatio.model is a model that regresses taxa against the categorical experimental condition. values of 1 are interpreted to be a perfect retention of relationship through sampling and normalization; values between 0 and 1 are underestimation of the strength of the relationship; values over 1 are overestimation. So, let’s look at how mean abundance relates to accuracy of the linear model on a taxon-by-taxon basis:
plot(log(model$model$SpeciesMeta$mean_abundance),model$QSeq0.5$lmRatiotab, col=gray(model$model$SpeciesMeta$M.Eval),
main="QSeq0.5 R-ratio of Taxa vs Environment", xlab="Taxon Prevalence", ylab="R-Ratio")
plot(log(model$model$SpeciesMeta$mean_abundance),model$QSeq100$lmRatiotab, col=gray(model$model$SpeciesMeta$M.Eval),
main="QSeq100 R-ratio of Taxa vs Environment", xlab="Taxon Prevalence", ylab="R-Ratio")
Notice that QSeq0.5 has many more taxa that have completely lost the relationship between taxa and the environment, and a few where the relationship is over estimated. QSeq100 has none that have lost their relationship completely. While QSeq has more taxa that have an over-estimated relationship with the environmental variable, the accuracy of the estimate is still high, with most of those taxa still being within 10% error. Here is the same plots but for the categorical variables:
plot(log(model$model$SpeciesMeta$mean_abundance),model$QSeq0.5$lmRatiotab.model, col=gray(model$model$SpeciesMeta$M.Eval),
main="QSeq0.5 R-ratio of Taxa vs Category", xlab="Taxon Prevalence", ylab="R-Ratio")
plot(log(model$model$SpeciesMeta$mean_abundance),model$QSeq100$lmRatiotab.model, col=gray(model$model$SpeciesMeta$M.Eval),
main="QSeq100 R-ratio of Taxa vs Category", xlab="Taxon Prevalence", ylab="R-Ratio")
We can clearly see from both linear model R-Ratio plots that there are a number of taxa for which we lost completely any relationship. These were likely taxa that were rounded out of the community in QSeq0.5 but not QSeq100. We can also see that overall the general pattern of relationships is maintained across the rest of the taxa. The rate of overestimation of the relationship between taxa and explanitory variables also remains the same
You may notice that certain taxa have an R squared of 0; some of them improve as we increase the overall scaling factor. This happens when taxa are very low abundance in a particular sample. If their count abundance is less than 0.5, they get rounded down to 0. So ideally we want to pick a scaling value that lets us keep all the information from sampling (i.e. such that in all samples, the minimum taxon has a count of at least 1). This is an important observation if we want to use this method on a real dataset because it gives us a criteria for choosing what our scaling factor will be.
We can see qualitatively that our higher QSeq methods increase the accuracy of our taxon-specific models by a small margin. We can evaluate this statistically:
levenetest<-data.frame("ratio"=c(model$QSeq0.5$lmRatiotab, model$QSeq100$lmRatiotab), "method"=c(rep("raw", length(model$raw$lmRatiotab)), rep("QSeq", length(model$QSeq3$lmRatiotab))))
car::leveneTest(ratio ~ method, data = levenetest)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 4.4617 0.03564 *
## 254
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
var(model$QSeq0.5$lmRatiotab)
## [1] 0.1127676
var(model$QSeq100$lmRatiotab)
## [1] 0.06331075
This indicates that there is greater variation in the lmRatio values in the QSeq0.5 versus the QSeq100. Remember, that the deviation in value from 1 represents lost accuracy in the information being retained; we can therefore interpret higher variance as being lower accuracy in the relationships being modeled after the transformation. This method provides a solid evidence-based approach for optimizing normalization methods.
It might be instructional at this point to look at the same distribution without any normalization, to see how well the normalization improves our inference about the relationship of taxa to their environment:
plot(model$model$SpeciesMeta$prevalence,model$raw$lmRatiotab, col=gray(model$model$SpeciesMeta$M.Eval),
main="Not normalized vs Environment", xlab="Taxon Prevalence", ylab="Rsquared-Ratio")
plot(model$model$SpeciesMeta$prevalence,model$QSeq100$lmRatiotab, col=gray(model$model$SpeciesMeta$M.Eval),
main="QSeq100 vs Environment", xlab="Taxon Prevalence", ylab="Rsquared-Ratio")
plot(model$model$SpeciesMeta$prevalence,model$raw$lmRatiotab.model, col=gray(model$model$SpeciesMeta$M.Eval),
main="Not normalized vs Category", xlab="Taxon Prevalence", ylab="Rsquared-Ratio")
plot(model$model$SpeciesMeta$prevalence,model$QSeq100$lmRatiotab.model, col=gray(model$model$SpeciesMeta$M.Eval),
main="QSeq100 vs Category", xlab="Taxon Prevalence", ylab="Rsquared-Ratio")
We can see that sometimes the differences are subtle, but other times normalization can remove large artifacts.
Now let’s look at how relationships among taxa are affected by normalization (or lack therof). We can access the R-Ratio for a correlation among taxa. Typically the first thing that we do for a network analysis is to correlate taxa to one another. Model.Microbiome does this automatically, using a pearson correlation. All we need to do is access this information using the getTaxCor.Tab function. This function outputs an object that contains a table of variances and median correlation ratios. These are calculated in a similar fashion as the correlation ratios of taxa to the environment;
let a be the correlation coefficient between two taxa in the reference. let b be the correlation coefficient between two taxa after normalization treatment.
The correlation ratio is defined as b/a
NOTE: because occasionally a = 0, resulting in an undefined result we have chosen to convert all a = 0 -> a = min(a/10) in order to remove infinite values, retain the information that these instances result in mis-estimation of the relationship between taxa, and without punishing the misestimation too harshly (an infinite value pushes the mean to infinite, even if only one infinite value exists in the dataset)
Thus we are extracting the variance of all ratios for each normalization method; and the median ratio of all normalization methods
model$raw$taxCor.Ratio
## Var1 Var2 value
## 1 spp101 spp101 1.000000e+00
## 2 spp103 spp101 5.419079e-01
## 3 spp104 spp101 8.421576e-01
## 4 spp110 spp101 8.421576e-01
## 5 spp114 spp101 -9.531800e+00
## 6 spp116 spp101 8.421576e-01
## 7 spp126 spp101 5.420756e-02
## 8 spp133 spp101 5.438753e-01
## 9 spp139 spp101 7.187863e-01
## 10 spp152 spp101 6.020929e-01
## 11 spp165 spp101 6.457355e-01
## 12 spp168 spp101 7.081003e-01
## 13 spp169 spp101 1.027350e+00
## 14 spp177 spp101 1.772151e+00
## 15 spp185 spp101 5.972171e-01
## 16 spp2 spp101 6.856194e-01
## 17 spp204 spp101 7.121531e-01
## 18 spp209 spp101 7.092280e-01
## 19 spp21 spp101 5.034817e-01
## 20 spp216 spp101 5.823785e-01
## 21 spp22 spp101 6.832585e-01
## 22 spp220 spp101 8.421576e-01
## 23 spp231 spp101 8.421576e-01
## 24 spp232 spp101 8.421576e-01
## 25 spp238 spp101 8.421576e-01
## 26 spp243 spp101 2.880587e-01
## 27 spp251 spp101 6.061929e-01
## 28 spp252 spp101 8.541317e-01
## 29 spp253 spp101 8.421576e-01
## 30 spp256 spp101 6.740636e-01
## 31 spp257 spp101 6.473767e-01
## 32 spp259 spp101 8.421576e-01
## 33 spp267 spp101 9.711193e-01
## 34 spp27 spp101 8.421576e-01
## 35 spp271 spp101 7.138182e-01
## 36 spp272 spp101 8.421576e-01
## 37 spp273 spp101 6.879661e-01
## 38 spp279 spp101 4.982060e-01
## 39 spp285 spp101 4.731564e-01
## 40 spp286 spp101 8.421576e-01
## 41 spp290 spp101 1.070465e+00
## 42 spp293 spp101 4.982060e-01
## 43 spp296 spp101 -1.664746e-01
## 44 spp301 spp101 6.004743e-01
## 45 spp305 spp101 8.421576e-01
## 46 spp306 spp101 6.750509e-01
## 47 spp308 spp101 1.724700e+00
## 48 spp310 spp101 7.994843e-01
## 49 spp316 spp101 8.421576e-01
## 50 spp319 spp101 7.358415e-01
## 51 spp32 spp101 7.473883e-01
## 52 spp329 spp101 4.268185e-01
## 53 spp33 spp101 4.966536e-01
## 54 spp332 spp101 8.421576e-01
## 55 spp337 spp101 6.552562e-01
## 56 spp339 spp101 8.421576e-01
## 57 spp340 spp101 6.756354e-01
## 58 spp344 spp101 8.795363e-02
## 59 spp349 spp101 8.421576e-01
## 60 spp353 spp101 8.421576e-01
## 61 spp354 spp101 7.401367e-01
## 62 spp36 spp101 5.420188e-01
## 63 spp362 spp101 7.263913e-01
## 64 spp366 spp101 7.408176e-01
## 65 spp370 spp101 8.977445e-01
## 66 spp373 spp101 8.421576e-01
## 67 spp375 spp101 8.421576e-01
## 68 spp380 spp101 8.421576e-01
## 69 spp381 spp101 1.005913e+00
## 70 spp384 spp101 6.546863e-01
## 71 spp386 spp101 8.643989e-01
## 72 spp387 spp101 7.303813e-01
## 73 spp388 spp101 8.421576e-01
## 74 spp389 spp101 8.063377e-01
## 75 spp392 spp101 1.170364e+00
## 76 spp393 spp101 9.293574e-01
## 77 spp394 spp101 6.905865e-01
## 78 spp395 spp101 8.421576e-01
## 79 spp398 spp101 8.421576e-01
## 80 spp4 spp101 8.421576e-01
## 81 spp40 spp101 5.679842e-01
## 82 spp406 spp101 8.808432e-01
## 83 spp407 spp101 9.520397e-01
## 84 spp410 spp101 8.421576e-01
## 85 spp416 spp101 7.040233e-01
## 86 spp418 spp101 3.593440e-01
## 87 spp421 spp101 4.592971e-01
## 88 spp439 spp101 1.200846e-01
## 89 spp457 spp101 8.421576e-01
## 90 spp459 spp101 7.381811e-01
## 91 spp467 spp101 1.028389e+00
## 92 spp469 spp101 9.343638e-01
## 93 spp475 spp101 3.837656e-01
## 94 spp481 spp101 5.823814e-01
## 95 spp483 spp101 4.917741e-01
## 96 spp490 spp101 9.206078e-01
## 97 spp492 spp101 8.411929e-01
## 98 spp501 spp101 9.020396e-01
## 99 spp503 spp101 7.308994e-01
## 100 spp51 spp101 8.421576e-01
## 101 spp514 spp101 7.269156e-01
## 102 spp515 spp101 1.887819e-01
## 103 spp519 spp101 5.446328e-01
## 104 spp521 spp101 1.014201e+00
## 105 spp527 spp101 6.259040e-01
## 106 spp537 spp101 2.553234e-01
## 107 spp547 spp101 4.801151e-01
## 108 spp555 spp101 8.486684e-01
## 109 spp559 spp101 -8.351875e+00
## 110 spp565 spp101 8.421576e-01
## 111 spp567 spp101 5.420756e-02
## 112 spp569 spp101 9.460648e-01
## 113 spp59 spp101 7.205076e-01
## 114 spp6 spp101 8.421576e-01
## 115 spp60 spp101 7.476396e-01
## 116 spp601 spp101 6.266669e-01
## 117 spp604 spp101 1.032418e+00
## 118 spp62 spp101 6.326916e-01
## 119 spp634 spp101 5.117990e-02
## 120 spp639 spp101 5.199854e-01
## 121 spp653 spp101 8.421576e-01
## 122 spp654 spp101 6.857520e-01
## 123 spp659 spp101 8.421576e-01
## 124 spp668 spp101 8.421576e-01
## 125 spp679 spp101 1.270305e+00
## 126 spp684 spp101 8.332113e-01
## 127 spp85 spp101 5.133592e-01
## 128 spp9 spp101 6.946194e-01
## 129 spp101 spp103 5.419079e-01
## 130 spp103 spp103 1.000000e+00
## 131 spp104 spp103 7.893535e-01
## 132 spp110 spp103 -5.793469e-01
## 133 spp114 spp103 5.814693e-01
## 134 spp116 spp103 4.604862e+00
## 135 spp126 spp103 8.091009e-01
## 136 spp133 spp103 2.395228e+00
## 137 spp139 spp103 -2.246710e-01
## 138 spp152 spp103 3.835818e-01
## 139 spp165 spp103 1.116076e+00
## 140 spp168 spp103 1.692304e+00
## 141 spp169 spp103 -5.007487e-01
## 142 spp177 spp103 -2.438024e-02
## 143 spp185 spp103 -5.458277e+00
## 144 spp2 spp103 2.578335e+00
## 145 spp204 spp103 6.371383e-01
## 146 spp209 spp103 3.030311e+00
## 147 spp21 spp103 -1.395390e-01
## 148 spp216 spp103 1.270420e-01
## 149 spp22 spp103 -3.417033e-01
## 150 spp220 spp103 7.893535e-01
## 151 spp231 spp103 4.688036e+00
## 152 spp232 spp103 7.893535e-01
## 153 spp238 spp103 8.595246e-01
## 154 spp243 spp103 3.483812e-01
## 155 spp251 spp103 2.597851e+00
## 156 spp252 spp103 6.125069e+00
## 157 spp253 spp103 7.893535e-01
## 158 spp256 spp103 2.100503e+00
## 159 spp257 spp103 4.591746e-01
## 160 spp259 spp103 7.893535e-01
## 161 spp267 spp103 -1.550295e-02
## 162 spp27 spp103 7.893535e-01
## 163 spp271 spp103 1.722603e+00
## 164 spp272 spp103 7.893535e-01
## 165 spp273 spp103 1.140014e-01
## 166 spp279 spp103 8.538700e-01
## 167 spp285 spp103 4.697699e-01
## 168 spp286 spp103 -6.493974e-01
## 169 spp290 spp103 6.035694e-01
## 170 spp293 spp103 8.538700e-01
## 171 spp296 spp103 1.436286e+00
## 172 spp301 spp103 -1.603606e-01
## 173 spp305 spp103 1.914910e+00
## 174 spp306 spp103 6.998952e-01
## 175 spp308 spp103 7.338625e-01
## 176 spp310 spp103 -4.014356e+00
## 177 spp316 spp103 4.688036e+00
## 178 spp319 spp103 2.960506e-01
## 179 spp32 spp103 2.519430e+00
## 180 spp329 spp103 1.333777e+00
## 181 spp33 spp103 -6.640161e-01
## 182 spp332 spp103 7.893535e-01
## 183 spp337 spp103 6.465893e-01
## 184 spp339 spp103 2.726549e-01
## 185 spp340 spp103 1.798610e+00
## 186 spp344 spp103 4.910030e-01
## 187 spp349 spp103 7.893535e-01
## 188 spp353 spp103 -1.066280e-01
## 189 spp354 spp103 2.847597e+00
## 190 spp36 spp103 5.080337e-01
## 191 spp362 spp103 -1.830827e-01
## 192 spp366 spp103 -1.841990e-01
## 193 spp370 spp103 -1.275742e-01
## 194 spp373 spp103 1.557003e+00
## 195 spp375 spp103 7.893535e-01
## 196 spp380 spp103 4.604862e+00
## 197 spp381 spp103 5.453197e-01
## 198 spp384 spp103 1.562127e+00
## 199 spp386 spp103 -2.561950e+00
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## 1929 spp139 spp2 6.948581e-01
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## 1955 spp271 spp2 8.522017e-01
## 1956 spp272 spp2 8.141224e-01
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## 1990 spp384 spp2 4.426585e+00
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## 2008 spp439 spp2 2.994753e+00
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## 2012 spp469 spp2 3.469275e-01
## 2013 spp475 spp2 3.709902e-01
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## 2018 spp501 spp2 8.720110e-01
## 2019 spp503 spp2 4.288378e-01
## 2020 spp51 spp2 6.022663e-01
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## 15998 spp684 spp679 9.470460e-01
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## 16003 spp104 spp684 1.258427e+00
## 16004 spp110 spp684 3.559431e+00
## 16005 spp114 spp684 -6.800635e-01
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## 16009 spp139 spp684 4.611695e-02
## 16010 spp152 spp684 1.004425e-01
## 16011 spp165 spp684 8.900257e-01
## 16012 spp168 spp684 8.500038e-01
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## 16019 spp21 spp684 2.753390e-01
## 16020 spp216 spp684 3.224398e-01
## 16021 spp22 spp684 4.902638e-01
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## 16029 spp253 spp684 7.471512e-01
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## 16031 spp257 spp684 2.975103e-01
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## 16199 spp386 spp85 1.394137e+00
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## 16201 spp388 spp85 -1.395194e+01
## 16202 spp389 spp85 3.566750e-01
## 16203 spp392 spp85 -1.154700e+00
## 16204 spp393 spp85 5.749010e-01
## 16205 spp394 spp85 4.998650e-01
## 16206 spp395 spp85 6.095761e-01
## 16207 spp398 spp85 6.095761e-01
## 16208 spp4 spp85 6.095761e-01
## 16209 spp40 spp85 -2.049065e-01
## 16210 spp406 spp85 6.055437e-01
## 16211 spp407 spp85 -2.952093e-01
## 16212 spp410 spp85 -1.192649e-01
## 16213 spp416 spp85 5.095909e-01
## 16214 spp418 spp85 2.601028e-01
## 16215 spp421 spp85 3.401859e-01
## 16216 spp439 spp85 5.752594e-01
## 16217 spp457 spp85 -3.928215e-01
## 16218 spp459 spp85 -1.355516e+00
## 16219 spp467 spp85 5.189393e-01
## 16220 spp469 spp85 9.562354e+00
## 16221 spp475 spp85 -1.486274e-01
## 16222 spp481 spp85 -1.028399e+00
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## 16234 spp537 spp85 4.877903e-01
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## 16252 spp668 spp85 6.095761e-01
## 16253 spp679 spp85 4.273457e-01
## 16254 spp684 spp85 6.666724e-01
## 16255 spp85 spp85 1.000000e+00
## 16256 spp9 spp85 -1.248292e+00
## 16257 spp101 spp9 6.946194e-01
## 16258 spp103 spp9 2.552735e+00
## 16259 spp104 spp9 8.248093e-01
## 16260 spp110 spp9 8.248093e-01
## 16261 spp114 spp9 3.476273e-01
## 16262 spp116 spp9 8.614376e-01
## 16263 spp126 spp9 8.248093e-01
## 16264 spp133 spp9 9.717772e-01
## 16265 spp139 spp9 7.039795e-01
## 16266 spp152 spp9 5.896899e-01
## 16267 spp165 spp9 3.516240e-01
## 16268 spp168 spp9 5.221805e-01
## 16269 spp169 spp9 3.098150e-01
## 16270 spp177 spp9 -4.211103e-01
## 16271 spp185 spp9 5.849145e-01
## 16272 spp2 spp9 9.868882e-01
## 16273 spp204 spp9 3.156557e-01
## 16274 spp209 spp9 4.949015e-01
## 16275 spp21 spp9 4.931101e-01
## 16276 spp216 spp9 5.703816e-01
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## 16278 spp220 spp9 8.248093e-01
## 16279 spp231 spp9 1.937050e+00
## 16280 spp232 spp9 8.248093e-01
## 16281 spp238 spp9 8.248093e-01
## 16282 spp243 spp9 3.956717e-01
## 16283 spp251 spp9 1.037339e+00
## 16284 spp252 spp9 8.365368e-01
## 16285 spp253 spp9 8.248093e-01
## 16286 spp256 spp9 6.601781e-01
## 16287 spp257 spp9 6.340409e-01
## 16288 spp259 spp9 8.248093e-01
## 16289 spp267 spp9 9.984492e-02
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## 16291 spp271 spp9 9.714228e-01
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## 16293 spp273 spp9 -8.288093e-02
## 16294 spp279 spp9 8.248093e-01
## 16295 spp285 spp9 5.969026e-01
## 16296 spp286 spp9 8.248093e-01
## 16297 spp290 spp9 1.048414e+00
## 16298 spp293 spp9 8.248093e-01
## 16299 spp296 spp9 2.998671e-01
## 16300 spp301 spp9 5.881047e-01
## 16301 spp305 spp9 4.930905e-01
## 16302 spp306 spp9 6.611450e-01
## 16303 spp308 spp9 8.248093e-01
## 16304 spp310 spp9 7.830152e-01
## 16305 spp316 spp9 1.937050e+00
## 16306 spp319 spp9 7.206834e-01
## 16307 spp32 spp9 9.371799e-01
## 16308 spp329 spp9 3.635226e+00
## 16309 spp33 spp9 4.864227e-01
## 16310 spp332 spp9 8.248093e-01
## 16311 spp337 spp9 -7.115028e-01
## 16312 spp339 spp9 1.977209e-01
## 16313 spp340 spp9 -2.678483e+00
## 16314 spp344 spp9 7.531135e-01
## 16315 spp349 spp9 8.248093e-01
## 16316 spp353 spp9 8.248093e-01
## 16317 spp354 spp9 1.008825e+00
## 16318 spp36 spp9 5.308533e-01
## 16319 spp362 spp9 7.114279e-01
## 16320 spp366 spp9 7.255570e-01
## 16321 spp370 spp9 8.792512e-01
## 16322 spp373 spp9 8.248093e-01
## 16323 spp375 spp9 8.248093e-01
## 16324 spp380 spp9 8.614376e-01
## 16325 spp381 spp9 7.023397e-01
## 16326 spp384 spp9 4.662608e+00
## 16327 spp386 spp9 8.465925e-01
## 16328 spp387 spp9 1.016551e+00
## 16329 spp388 spp9 1.937050e+00
## 16330 spp389 spp9 1.823601e+01
## 16331 spp392 spp9 7.674135e-01
## 16332 spp393 spp9 7.778909e-01
## 16333 spp394 spp9 6.763606e-01
## 16334 spp395 spp9 8.614376e-01
## 16335 spp398 spp9 8.248093e-01
## 16336 spp4 spp9 9.271948e-01
## 16337 spp40 spp9 5.562838e-01
## 16338 spp406 spp9 8.193530e-01
## 16339 spp407 spp9 9.324279e-01
## 16340 spp410 spp9 8.248093e-01
## 16341 spp416 spp9 6.895206e-01
## 16342 spp418 spp9 4.859402e-01
## 16343 spp421 spp9 1.570648e-01
## 16344 spp439 spp9 3.000285e+00
## 16345 spp457 spp9 8.248093e-01
## 16346 spp459 spp9 9.597135e-01
## 16347 spp467 spp9 7.021698e-01
## 16348 spp469 spp9 3.611247e-01
## 16349 spp475 spp9 3.758602e-01
## 16350 spp481 spp9 8.037026e-01
## 16351 spp483 spp9 4.816437e-01
## 16352 spp490 spp9 5.181962e-01
## 16353 spp492 spp9 6.120676e-01
## 16354 spp501 spp9 8.834578e-01
## 16355 spp503 spp9 6.390905e-01
## 16356 spp51 spp9 9.271948e-01
## 16357 spp514 spp9 7.505062e-01
## 16358 spp515 spp9 1.981961e+00
## 16359 spp519 spp9 5.334135e-01
## 16360 spp521 spp9 6.000730e-01
## 16361 spp527 spp9 7.392086e-01
## 16362 spp537 spp9 3.352372e+00
## 16363 spp547 spp9 2.123894e-01
## 16364 spp555 spp9 8.311861e-01
## 16365 spp559 spp9 7.598761e-01
## 16366 spp565 spp9 8.248093e-01
## 16367 spp567 spp9 8.248093e-01
## 16368 spp569 spp9 7.894693e-01
## 16369 spp59 spp9 1.270285e+00
## 16370 spp6 spp9 8.248093e-01
## 16371 spp60 spp9 7.322384e-01
## 16372 spp601 spp9 6.137577e-01
## 16373 spp604 spp9 1.011151e+00
## 16374 spp62 spp9 3.221037e+00
## 16375 spp634 spp9 2.507259e+00
## 16376 spp639 spp9 9.398190e-01
## 16377 spp653 spp9 4.930905e-01
## 16378 spp654 spp9 1.004722e+00
## 16379 spp659 spp9 8.248093e-01
## 16380 spp668 spp9 8.248093e-01
## 16381 spp679 spp9 5.782357e-01
## 16382 spp684 spp9 -1.279324e-01
## 16383 spp85 spp9 -1.248292e+00
## 16384 spp9 spp9 1.000000e+00
Negative values indicate a negative relationship between the relationship among taxa in the reference compared to the treatment. Ideally all relationships should be 1 if the information is perfectly preserved. We can subset the dataset by specific taxa, and use metadata about those taxa to better understand why the relationships change. If we look at taxon 153, we see that it exists in 22 sites. We can look at how the prevalence and abundance of other taxa relate to the predicted relationship between the taxa. First let’s identify low prevalence and high prevalence taxa.
# create values for subsetting
nm<-rownames(model$model$SpeciesMeta)
nm.h<-nm[model$model$SpeciesMeta$prevalence>20]
nm.l<-nm[model$model$SpeciesMeta$prevalence==1]
table(rownames(model$model$SpeciesMeta)==model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.l[[1]],1])
##
## TRUE
## 128
# plot vs prevalence
plot(model$model$SpeciesMeta$prevalence,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.h[[1]],3], xlab="Prevalence", ylab="taxcor.Ratio")
plot(model$model$SpeciesMeta$mean_abundance,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.h[[1]],3], xlab="mean Abundance", ylab="taxcor.Ratio")
plot(model$model$SpeciesMeta$sd_abundance,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.h[[1]],3], xlab="SD Abundance", ylab="taxcor.Ratio")
We can see in general, the largest errors come from where the prevalence and mean abundance are both low. However, in this example the one difference is a highly prevalent, but low abundance taxon. We can examine how this pattern holds up on a low prevalence taxon.
# check taxa are in the right order
table(rownames(model$model$SpeciesMeta)==model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.l[[1]],1])
##
## TRUE
## 128
# plot vs prevalence
plot(model$model$SpeciesMeta$prevalence,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.l[[1]],3], xlab="Prevalence", ylab="taxcor.Ratio")
plot(model$model$SpeciesMeta$mean_abundance,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.l[[1]],3], xlab="mean Abundance", ylab="taxcor.Ratio")
plot(model$model$SpeciesMeta$sd_abundance,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.l[[1]],3], xlab="SD Abundance", ylab="taxcor.Ratio")
It is important to note that there are some negative values. The Taxcor is a pearson correlation. The other metrics use a R-sqaured value, which precludes negatives. In this case there is an interpretation: the relationship between taxa is opposite in the reference than in the normalized data. This would be interpreted as potentially a false positive relationship if the relationship is strong enough after normalization.
Model.Microbiome includes several R-ratio metrics for whole community patterns. These are based on the PERMANOVA r-squared value. Model.Microbiome conducts a PERMANOVA of each environmental factor and the categorical factor against a Bray-Curtis transformation of the count table. These are done separately because order of addition of the factors in the model influences the model outcomes; it is easiest to get comparable results run each factor in isolation. For example:
model$raw$PERMANOVA$F1
##
## Call:
## adonis(formula = x ~ F1, data = y)
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## F1 1 1.0582 1.05818 4.2325 0.13131 0.001 ***
## Residuals 28 7.0003 0.25001 0.86869
## Total 29 8.0585 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
The R squared part of the table is taken as a ratio of the reference:
model$raw$PERMANOVA$F1Rratio
## R ratio Residual ratio total
## 0.7448459 1.0546095 1.0000000
We can examine how well each of the environmental and categorical factors are maintained:
model$raw$PERMANOVA$CategoryRratio
## R ratio Residual ratio total
## 0.9748416 1.2468360 1.0000000
model$raw$PERMANOVA$F2Rratio
## R ratio Residual ratio total
## 0.9053624 1.0152625 1.0000000
model$raw$PERMANOVA$F3Rratio
## R ratio Residual ratio total
## 0.6974213 1.1111097 1.0000000
model$raw$PERMANOVA$F4Rratio
## R ratio Residual ratio total
## 0.5404463 1.0310548 1.0000000
model$raw$PERMANOVA$F5Rratio
## R ratio Residual ratio total
## 0.9159684 1.0062026 1.0000000
And of course, we can plot an ordination:
bray_NMDS = ordinate(model$QSeq10$comm, "NMDS", "bray")
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1642471
## Run 1 stress 0.176735
## Run 2 stress 0.1727819
## Run 3 stress 0.1735785
## Run 4 stress 0.1642471
## ... Procrustes: rmse 1.927883e-05 max resid 9.003283e-05
## ... Similar to previous best
## Run 5 stress 0.1642471
## ... Procrustes: rmse 2.898575e-05 max resid 0.0001354968
## ... Similar to previous best
## Run 6 stress 0.1728475
## Run 7 stress 0.1745
## Run 8 stress 0.1642471
## ... Procrustes: rmse 2.107593e-05 max resid 9.877328e-05
## ... Similar to previous best
## Run 9 stress 0.173992
## Run 10 stress 0.1745764
## Run 11 stress 0.1739759
## Run 12 stress 0.1735802
## Run 13 stress 0.1745003
## Run 14 stress 0.1740196
## Run 15 stress 0.1642471
## ... Procrustes: rmse 2.619253e-05 max resid 0.0001229358
## ... Similar to previous best
## Run 16 stress 0.1816305
## Run 17 stress 0.1918856
## Run 18 stress 0.1730667
## Run 19 stress 0.1739868
## Run 20 stress 0.1738055
## *** Solution reached
plot_ordination(model$QSeq10$comm, bray_NMDS, "samples", color="Factor")
We can compare the ordination
bray_NMDS.ref = ordinate(model$model$comm, "NMDS", "bray")
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1032647
## Run 1 stress 0.1352588
## Run 2 stress 0.1032647
## ... Procrustes: rmse 2.186653e-06 max resid 5.276753e-06
## ... Similar to previous best
## Run 3 stress 0.2177992
## Run 4 stress 0.135307
## Run 5 stress 0.1032647
## ... Procrustes: rmse 2.893928e-06 max resid 7.357229e-06
## ... Similar to previous best
## Run 6 stress 0.1032647
## ... Procrustes: rmse 5.732468e-06 max resid 1.410858e-05
## ... Similar to previous best
## Run 7 stress 0.1032647
## ... New best solution
## ... Procrustes: rmse 1.921246e-06 max resid 3.981697e-06
## ... Similar to previous best
## Run 8 stress 0.1032647
## ... Procrustes: rmse 2.514277e-06 max resid 6.607881e-06
## ... Similar to previous best
## Run 9 stress 0.1032647
## ... Procrustes: rmse 6.23875e-06 max resid 1.361394e-05
## ... Similar to previous best
## Run 10 stress 0.1032647
## ... Procrustes: rmse 2.254725e-06 max resid 8.186324e-06
## ... Similar to previous best
## Run 11 stress 0.135307
## Run 12 stress 0.1032647
## ... Procrustes: rmse 1.557505e-06 max resid 4.857962e-06
## ... Similar to previous best
## Run 13 stress 0.1032647
## ... New best solution
## ... Procrustes: rmse 1.408713e-06 max resid 3.149888e-06
## ... Similar to previous best
## Run 14 stress 0.1032647
## ... Procrustes: rmse 1.802466e-06 max resid 4.880144e-06
## ... Similar to previous best
## Run 15 stress 0.1032647
## ... Procrustes: rmse 8.580318e-07 max resid 2.48826e-06
## ... Similar to previous best
## Run 16 stress 0.1032647
## ... Procrustes: rmse 5.220029e-06 max resid 1.34319e-05
## ... Similar to previous best
## Run 17 stress 0.135307
## Run 18 stress 0.1032647
## ... Procrustes: rmse 1.06033e-06 max resid 2.527323e-06
## ... Similar to previous best
## Run 19 stress 0.3915013
## Run 20 stress 0.135307
## *** Solution reached
plot_ordination(model$model$comm, bray_NMDS.ref, "samples", color="Factor")
bray_NMDS.raw = ordinate(model$raw$comm, "NMDS", "bray")
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1590721
## Run 1 stress 0.1594203
## ... Procrustes: rmse 0.01708649 max resid 0.04928656
## Run 2 stress 0.15942
## ... Procrustes: rmse 0.01702016 max resid 0.04931327
## Run 3 stress 0.1588214
## ... New best solution
## ... Procrustes: rmse 0.005492935 max resid 0.02168543
## Run 4 stress 0.1590721
## ... Procrustes: rmse 0.005474916 max resid 0.02160621
## Run 5 stress 0.1591219
## ... Procrustes: rmse 0.01181834 max resid 0.04750845
## Run 6 stress 0.1588214
## ... Procrustes: rmse 6.686958e-05 max resid 0.0002144158
## ... Similar to previous best
## Run 7 stress 0.1777053
## Run 8 stress 0.1594201
## Run 9 stress 0.2101728
## Run 10 stress 0.1776931
## Run 11 stress 0.1591219
## ... Procrustes: rmse 0.01180074 max resid 0.047568
## Run 12 stress 0.1787498
## Run 13 stress 0.1591231
## ... Procrustes: rmse 0.01181595 max resid 0.04756514
## Run 14 stress 0.2089419
## Run 15 stress 0.1591227
## ... Procrustes: rmse 0.01188552 max resid 0.04700879
## Run 16 stress 0.1628561
## Run 17 stress 0.177478
## Run 18 stress 0.1588216
## ... Procrustes: rmse 0.0001685084 max resid 0.0005873744
## ... Similar to previous best
## Run 19 stress 0.1762812
## Run 20 stress 0.1588216
## ... Procrustes: rmse 0.0001306327 max resid 0.0004323713
## ... Similar to previous best
## *** Solution reached
plot_ordination(model$raw$comm, bray_NMDS.raw, "samples", color="Factor")
bray_NMDS.Q = ordinate(model$QSeq10$comm, "NMDS", "bray")
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1642471
## Run 1 stress 0.1700293
## Run 2 stress 0.1748909
## Run 3 stress 0.1748592
## Run 4 stress 0.1642472
## ... Procrustes: rmse 6.289248e-05 max resid 0.0002962919
## ... Similar to previous best
## Run 5 stress 0.169858
## Run 6 stress 0.1755374
## Run 7 stress 0.2169519
## Run 8 stress 0.175577
## Run 9 stress 0.1732039
## Run 10 stress 0.1748605
## Run 11 stress 0.1683357
## Run 12 stress 0.1738102
## Run 13 stress 0.1745003
## Run 14 stress 0.174891
## Run 15 stress 0.1732877
## Run 16 stress 0.1642471
## ... Procrustes: rmse 6.767525e-06 max resid 2.242044e-05
## ... Similar to previous best
## Run 17 stress 0.1739142
## Run 18 stress 0.1733601
## Run 19 stress 0.1642471
## ... Procrustes: rmse 1.48689e-05 max resid 4.819017e-05
## ... Similar to previous best
## Run 20 stress 0.1735793
## *** Solution reached
plot_ordination(model$QSeq10$comm, bray_NMDS.Q, "samples", color="Factor")
While it looks qualitatively like the QSeq ordination might be more accurate to the reference, it’s hard to tell. We can look at the R-Squared Ratio values to figure out which is more accurate. Here’s a spot test:
# raw
model$raw$PERMANOVA$F4Rratio
## R ratio Residual ratio total
## 0.5404463 1.0310548 1.0000000
# QSeq
model$QSeq10$PERMANOVA$F4Rratio
## R ratio Residual ratio total
## 1.0296519 0.9979962 1.0000000
# raw
model$raw$PERMANOVA$CategoryRratio
## R ratio Residual ratio total
## 0.9748416 1.2468360 1.0000000
# QSeq
model$QSeq10$PERMANOVA$CategoryRratio
## R ratio Residual ratio total
## 0.9748584 1.2466705 1.0000000
The category variables look nearly identical, whereas the environmental variables are much better modeled by the QSeq approach. In the next section, we’ll look at how to run multiple simulations to aggregate and statistically evaluate the differences of these approaches within the modeling environment.
Model.Microbiome has a wrapper that allows the user to iteratively generate random communities with the same experimental conditions. The inputs are the same as before, plus one aditional input to tell the function how many times to iterate. In this case we’ll do 10. We use suppressWarnings because the linear model often produces warnings when it has a perfect fit, and these can clutter the output.
model10<-suppressWarnings(BENCHMARK.MM(reps=10, commonN=30, groupN=20, singleN=5, D=500, V=250, method))
## [1] "spp selection complete"
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model10 is now a list object with 10 items, each one as a replicated simulation. This is the basis for us to be able to extract performance metrics and do statistical analyses to compare different normalization methods. Let’s look at some analyses that are possible when we can automate community generation.
We first extract the LII indicator with the function Summarize.LII(), then we melt the dataframe and do a statistical test on it:
model10.LIIsummary<-Summarize.LII(model10, method)
model10.LIIsummary<-melt(model10.LIIsummary, value.name = "Value")
summary(aov(Value~Var2 +Error(Var1/Var2), data=model10.LIIsummary)) # blocks of method are nested within each run
##
## Error: Var1
## Df Sum Sq Mean Sq F value Pr(>F)
## Residuals 9 0.08029 0.008921
##
## Error: Var1:Var2
## Df Sum Sq Mean Sq F value Pr(>F)
## Var2 5 0.06540 0.013079 55.8 <2e-16 ***
## Residuals 45 0.01055 0.000234
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(Value~Var2, data=model10.LIIsummary)) # ignoring the blocks bc TukeyHSD can't handle them. Still tells us which is most significant
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Value ~ Var2, data = model10.LIIsummary)
##
## $Var2
## diff lwr upr p adj
## QSeq1-QSeq0.5 -0.0501219646 -0.10431368 0.004069752 0.0852237
## QSeq2-QSeq0.5 -0.0822677819 -0.13645950 -0.028076065 0.0005276
## QSeq3-QSeq0.5 -0.0858370714 -0.14002879 -0.031645355 0.0002737
## QSeq10-QSeq0.5 -0.0909402152 -0.14513193 -0.036748499 0.0001049
## QSeq100-QSeq0.5 -0.0915970197 -0.14578874 -0.037405303 0.0000926
## QSeq2-QSeq1 -0.0321458173 -0.08633753 0.022045899 0.5042469
## QSeq3-QSeq1 -0.0357151068 -0.08990682 0.018476610 0.3857092
## QSeq10-QSeq1 -0.0408182506 -0.09500997 0.013373466 0.2433735
## QSeq100-QSeq1 -0.0414750551 -0.09566677 0.012716661 0.2279341
## QSeq3-QSeq2 -0.0035692895 -0.05776101 0.050622427 0.9999591
## QSeq10-QSeq2 -0.0086724333 -0.06286415 0.045519283 0.9969040
## QSeq100-QSeq2 -0.0093292378 -0.06352095 0.044862479 0.9956320
## QSeq10-QSeq3 -0.0051031438 -0.05929486 0.049088573 0.9997616
## QSeq100-QSeq3 -0.0057599483 -0.05995166 0.048431768 0.9995689
## QSeq100-QSeq10 -0.0006568044 -0.05484852 0.053534912 1.0000000
plot(TukeyHSD(aov(Value~Var2, data=model10.LIIsummary))) # visual of confidence intervals
Clearly, the worst performing method is QSeq0.5. This is likely because it effectively leads to undersampling because the detection threshold is so high. Ideally we should choose a threshold value for this method that is sufficiently high enough that all sequences that pass QC in our pipeline are included in the sampling, and not rounded to 0 in any sample.
Let’s look at how all these functionalities can be tied together into a comprehensive test of the strengths (or weaknesses) of a normalization procedure.
We can look at the difference in PERMANOVA outputs:
model10.PCat<-Summarize.PERMANOVA.Rratio(model10, method, "CategoryRratio")
model10.PF1<-Summarize.PERMANOVA.Rratio(model10, method, "F1Rratio")
model10.PF2<-Summarize.PERMANOVA.Rratio(model10, method, "F2Rratio")
model10.PF3<-Summarize.PERMANOVA.Rratio(model10, method, "F3Rratio")
model10.PF4<-Summarize.PERMANOVA.Rratio(model10, method, "F4Rratio")
model10.PF5<-Summarize.PERMANOVA.Rratio(model10, method, "F5Rratio")
model10.PCat
## QSeq0.5 QSeq1 QSeq2 QSeq3 QSeq10 QSeq100
## rep1 0.9881261 0.9921541 0.9906986 0.9906381 0.9906119 0.9905366
## rep2 0.9884601 0.9878334 0.9886161 0.9883675 0.9883855 0.9883576
## rep3 0.9773214 0.9758738 0.9761179 0.9754467 0.9756708 0.9756950
## rep4 0.9677111 0.9718228 0.9701867 0.9705645 0.9705536 0.9704752
## rep5 0.9786398 0.9744689 0.9835492 0.9837772 0.9830671 0.9832764
## rep6 0.9744107 0.9764489 0.9773352 0.9774028 0.9770839 0.9770245
## rep7 0.9454088 0.9428646 0.9430017 0.9432314 0.9436426 0.9435475
## rep8 0.9877431 0.9839410 0.9849110 0.9846016 0.9847407 0.9846902
## rep9 0.9625179 0.9599453 0.9627013 0.9621837 0.9631343 0.9629951
## rep10 0.9646539 0.9640625 0.9632545 0.9637701 0.9637133 0.9636921
model10.PF1
## QSeq0.5 QSeq1 QSeq2 QSeq3 QSeq10 QSeq100
## rep1 0.9940840 0.9934145 0.9893918 0.9908630 0.9905719 0.9905493
## rep2 0.9775944 0.9807159 0.9826588 0.9815281 0.9818253 0.9820868
## rep3 0.9607124 0.9648225 0.9617297 0.9606411 0.9614017 0.9618031
## rep4 0.9743669 0.9692017 0.9683153 0.9693053 0.9687634 0.9685723
## rep5 0.9660457 0.9697915 0.9803968 0.9809564 0.9804135 0.9810709
## rep6 0.9778615 0.9745739 0.9744919 0.9742449 0.9746102 0.9746034
## rep7 0.8825335 0.9554767 0.9395778 0.9466839 0.9465838 0.9450085
## rep8 0.9718133 0.9713140 0.9724798 0.9722273 0.9723055 0.9723450
## rep9 0.9865882 0.9768376 0.9829539 0.9808733 0.9828734 0.9826030
## rep10 1.0158277 0.9991268 1.0055697 1.0048206 1.0045588 1.0044677
model10.PF2
## QSeq0.5 QSeq1 QSeq2 QSeq3 QSeq10 QSeq100
## rep1 0.9799895 0.9812818 0.9817546 0.9819709 0.9815427 0.9816409
## rep2 0.8764698 0.8781803 0.8802367 0.8779104 0.8790458 0.8789169
## rep3 1.0017515 0.9900001 0.9916000 0.9927568 0.9921086 0.9922794
## rep4 0.8995475 0.9058397 0.9012136 0.9031107 0.9024370 0.9029721
## rep5 1.0028392 0.9954152 0.9907016 0.9930782 0.9921611 0.9927491
## rep6 0.9867328 0.9887259 0.9873925 0.9890508 0.9885130 0.9886983
## rep7 0.9001474 0.9013847 0.9027194 0.9004918 0.9007936 0.9011432
## rep8 1.0074141 1.0069980 1.0096261 1.0082990 1.0096237 1.0093167
## rep9 0.8464131 0.8352390 0.8395098 0.8389328 0.8398993 0.8399103
## rep10 0.9497840 0.9494714 0.9493469 0.9483804 0.9492233 0.9493623
model10.PF3
## QSeq0.5 QSeq1 QSeq2 QSeq3 QSeq10 QSeq100
## rep1 0.9848215 0.9831319 0.9813946 0.9838849 0.9832748 0.9830854
## rep2 0.9761773 0.9753668 0.9766389 0.9759794 0.9760614 0.9759244
## rep3 0.9636922 0.9650680 0.9680485 0.9655182 0.9667143 0.9669182
## rep4 0.9489335 0.9558701 0.9567956 0.9557772 0.9557962 0.9555076
## rep5 0.9830311 0.9798891 0.9857959 0.9855101 0.9839962 0.9840539
## rep6 0.9255259 0.9303482 0.9301719 0.9288404 0.9288173 0.9286932
## rep7 0.9550585 0.9456604 0.9500324 0.9481839 0.9484077 0.9486378
## rep8 1.0009221 1.0004251 1.0019289 0.9990095 1.0004911 1.0005483
## rep9 0.9437705 0.9427215 0.9480851 0.9467291 0.9489354 0.9484727
## rep10 0.9606621 0.9591806 0.9541364 0.9560093 0.9557843 0.9554115
model10.PF4
## QSeq0.5 QSeq1 QSeq2 QSeq3 QSeq10 QSeq100
## rep1 1.0017923 1.0063945 1.0066836 1.0065263 1.0068951 1.0070115
## rep2 0.9614354 0.9622348 0.9600984 0.9606425 0.9601017 0.9602968
## rep3 0.9129965 0.9162085 0.9215214 0.9185178 0.9224934 0.9230714
## rep4 0.8975698 0.8915768 0.8935027 0.8945583 0.8962629 0.8961651
## rep5 0.9483157 0.9658663 0.9690047 0.9711747 0.9676485 0.9691194
## rep6 0.9400267 0.9295057 0.9291989 0.9291892 0.9299417 0.9301920
## rep7 0.9906456 0.9875782 0.9862913 0.9878382 0.9876615 0.9881708
## rep8 1.0884273 1.1111039 1.1055835 1.1068364 1.1064946 1.1072663
## rep9 0.9531081 0.9452595 0.9573413 0.9549065 0.9579801 0.9579369
## rep10 1.1489594 1.1523233 1.1396955 1.1398546 1.1378130 1.1390252
model10.PF5
## QSeq0.5 QSeq1 QSeq2 QSeq3 QSeq10 QSeq100
## rep1 0.9797332 0.9814054 0.9803288 0.9831601 0.9822573 0.9827244
## rep2 0.9000598 0.8952694 0.8964603 0.8969274 0.8978841 0.8982260
## rep3 0.9389391 0.9339514 0.9397234 0.9369315 0.9378527 0.9376733
## rep4 0.9785508 0.9757071 0.9753877 0.9763750 0.9762474 0.9762871
## rep5 0.9545484 0.9715013 0.9797089 0.9852004 0.9863477 0.9848842
## rep6 0.9664313 0.9565973 0.9616999 0.9557965 0.9586841 0.9586439
## rep7 0.9622637 0.9602673 0.9607610 0.9610094 0.9609488 0.9611259
## rep8 1.0151497 1.0238623 1.0208628 1.0217522 1.0193835 1.0193256
## rep9 0.9716080 0.9754491 0.9749067 0.9746532 0.9746371 0.9747223
## rep10 0.9220556 0.9218243 0.9255942 0.9239686 0.9228668 0.9231600
NOTE: In general, there are many outputs that a researcher may want to generate and summarize that we have not anticipated. Here are some functions for extracting the R-ratio from the linear models to give a template on the extraction method that works well with the object. This should give a means for researchers to extract and summarize any metric in any way they want. We will use both of these functions later in the analysis.
# get lmRatio ####
Summarize.lmRatiotab.Median<-function(trt, method){
Ftab<-matrix(NA, nrow = length(trt), ncol = length(method)) # make matrix
for(i in 1:length(trt)){
for(j in 1:length(method)){
Ftab[i,j]<-median(trt[[i]][[method[j]]]$lmRatiotab, na.rm=T)
#print(sum(trt[[i]][j]$PERMANOVA$aov.tab$F.Model))
}
}
rownames(Ftab)<-names(trt)
colnames(Ftab)<-method
Ftab
}
Summarize.lmRatiotab.Var<-function(trt, method){
Ftab<-matrix(NA, nrow = length(trt), ncol = length(method)) # make matrix
for(i in 1:length(trt)){
for(j in 1:length(method)){
Ftab[i,j]<-var(trt[[i]][[method[j]]]$lmRatiotab, na.rm=T)
#print(sum(trt[[i]][j]$PERMANOVA$aov.tab$F.Model))
}
}
rownames(Ftab)<-names(trt)
colnames(Ftab)<-method
Ftab
}
The following examples are an actual experiment run to identify biases associated with QSeq protocol, and to optimize QSeq for a number of different interpretive lenses.
Let’s say that we want to understand how the effect size of geographic structure within a community interacts with the performance of our normalization technique (or in the case of experimental design, what are the direct assemply effects of the treatment). Model.Microbiome gives us the power to vary the geographic structure/direct effects of the treatment on the community by determining the proportion of each sample that explicitly is determined by the grouping function:
# biogeography begin ####
model10.A<-suppressWarnings(BENCHMARK.MM(reps=10, commonN=53, groupN=1, singleN=1, D=500, V=250, method)) # essentially no filtration by group
model10.B<-suppressWarnings(BENCHMARK.MM(reps=10, commonN=35, groupN=15, singleN=5, D=500, V=250, method)) # ~27% filtration by the group
model10.C<-suppressWarnings(BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=250, method)) # ~36% filtration by the group
model10.D<-suppressWarnings(BENCHMARK.MM(reps=10, commonN=10, groupN=30, singleN=15, D=500, V=250, method)) # ~55% filtration by the group
First, let’s look at how the structure of the data might interact with our normalization strategy to influence how well information is retained. For this we will extract the LII value. As a reminder, LII correlates each taxon in the normalized dataset against it’s abundance in the reference dataset. The index itself is a sum of 1-R-squared; this means that low LII values mean that overall the R-squared of the taxa against their references were close to 1 (or little information was lost). Conversely, higher values indicate that a lot of information was lost.
# get LII Biogeography ####
method2<- c("raw", method) # add raw data to the methods list to extract it too
# extract the LII from each level of sparcity ####
SummaryLII.model10.A<-as.data.frame(Summarize.LII(model10.A,method2))
SummaryLII.model10.B<-as.data.frame(Summarize.LII(model10.B, method2))
SummaryLII.model10.C<-as.data.frame(Summarize.LII(model10.C, method2))
SummaryLII.model10.D<-as.data.frame(Summarize.LII(model10.D, method2))
# prepare data for merging datasets
SummaryLII.model10.A$Level<-c(rep(1,10))
SummaryLII.model10.A<-melt(SummaryLII.model10.A, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.B$Level<-c(rep(2,10))
SummaryLII.model10.B<-melt(SummaryLII.model10.B, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C$Level<-c(rep(3,10))
SummaryLII.model10.C<-melt(SummaryLII.model10.C, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.D$Level<-c(rep(4,10))
SummaryLII.model10.D<-melt(SummaryLII.model10.D, id.vars = "Level", measure.vars = method2)
# merge datasets
model10Levels<-do.call("rbind", list(SummaryLII.model10.A,SummaryLII.model10.B,SummaryLII.model10.C,SummaryLII.model10.D))
# summarize for plotting
model10Levels.summary2<-data_summary2(model10Levels, varname="value", groupnames=c("Level", "variable"))
model10Levels.summary1<-data_summary(model10Levels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(model10Levels.summary2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("LII Value (Median +/- min/max)")+
theme_classic()
ggplot(model10Levels.summary1, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("LII Value (Mean +/- standard dev)")+
theme_classic()
Here we can see clearly that the degree of structure in the dataset interacts with the normalization method to affect it’s accuracy. In general, less information is lost in QSeq methods, with the clear distinction being that QSeq0.5 performs worse than non normalizing under certain conditions. We can confirm this with a statistical test:
summary(aov(model10Levels$value~model10Levels$Level*model10Levels$variable))
TukeyHSD(aov(model10Levels$value~model10Levels$Level*model10Levels$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## model10Levels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## model10Levels$Level, model10Levels$variable
## Warning in TukeyHSD.aov(aov(model10Levels$value ~ model10Levels$Level * :
## 'which' specified some non-factors which will be dropped
Conclusion: we can see clearly that the degree of structure in the dataset interacts with the normalization method to affect how much information is retained on a taxon-by-taxon basis. In all cases the QSeq normalization method out performs un-normalized data at low structure, but at high levels of structure only QSeq2 and QSeq3 parameters continue to consistently outperform the raw variables. Remember that LII reports the degradation of R squared and so is a direct measure of lost information. But it doesn’t provide direct information about how well we can detect environmental drivers for the abundance of taxa.
In this case interpretation is a little more challenging, because we are less interested in the mean value, and more interested in the variance of the values. This is because our metric is a ratio of the R-squared (variance explained) of each taxon by the environment to the same measure of the taxon in the reference dataset. This tells us the relative accuracy with which the normalized dataset is predicting the relationship of each taxon to the environment. Ideally the mean value should be 1 (a perfect fit). But it is possible for the mean to be 1, but the deviation to be substantial if it is balanced in the positive and negative direction. In other words, if the error in the positive and negative direction are equal in size, then even if there is large error in those directions, the mean value will still be 1 (a perfect fit). Thus we might have a perfect fit of the mean, yet have no taxa that is accurately modeled. To account for this, we put larger emphasis on the variance using a levene’s test of equality of variance; but because variances may not be equally balanced in the positive and negative direction we are also still interested in changes in the average value. The two are necessary for accurate interpretation. We find especially for this analysis that outliers unduely affect the mean, so we prefer median for understanding the most common effect
Summarize.lmRatiotab.Var(model10.A, method2)
SM.lmRatio.model10.A<-as.data.frame(Summarize.lmRatiotab.Median(model10.A,method2))
SV.lmRatio.model10.A<-as.data.frame(Summarize.lmRatiotab.Var(model10.A,method2))
SM.lmRatio.model10.B<-as.data.frame(Summarize.lmRatiotab.Median(model10.B,method2))
SV.lmRatio.model10.B<-as.data.frame(Summarize.lmRatiotab.Var(model10.B,method2))
SM.lmRatio.model10.C<-as.data.frame(Summarize.lmRatiotab.Median(model10.C,method2))
SV.lmRatio.model10.C<-as.data.frame(Summarize.lmRatiotab.Var(model10.C,method2))
SM.lmRatio.model10.D<-as.data.frame(Summarize.lmRatiotab.Median(model10.D,method2))
SV.lmRatio.model10.D<-as.data.frame(Summarize.lmRatiotab.Var(model10.D,method2))
# prepare data for merging datasets
SM.lmRatio.model10.A$Level<-c(rep(1,10))
SV.lmRatio.model10.A$Level<-c(rep(1,10))
SM.lmRatio.model10.B$Level<-c(rep(2,10))
SV.lmRatio.model10.B$Level<-c(rep(2,10))
SM.lmRatio.model10.C$Level<-c(rep(3,10))
SV.lmRatio.model10.C$Level<-c(rep(3,10))
SM.lmRatio.model10.D$Level<-c(rep(4,10))
SV.lmRatio.model10.D$Level<-c(rep(4,10))
SM.lmRatio.model10.A<-melt(SM.lmRatio.model10.A, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.A<-melt(SV.lmRatio.model10.A, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.B<-melt(SM.lmRatio.model10.B, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.B<-melt(SV.lmRatio.model10.B, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C<-melt(SM.lmRatio.model10.C, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C<-melt(SV.lmRatio.model10.C, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.D<-melt(SM.lmRatio.model10.D, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.D<-melt(SV.lmRatio.model10.D, id.vars = "Level", measure.vars = method2)
# merge datasets
SM.lmRatio.model10Levels<-do.call("rbind", list(SM.lmRatio.model10.A,SM.lmRatio.model10.B,SM.lmRatio.model10.C,SM.lmRatio.model10.D))
SV.lmRatio.model10Levels<-do.call("rbind", list(SV.lmRatio.model10.A,SV.lmRatio.model10.B,SV.lmRatio.model10.C,SV.lmRatio.model10.D))
# summarize for plotting
SM.lmRatio.model10.p1<-data_summary(SM.lmRatio.model10Levels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10.p1<-data_summary(SV.lmRatio.model10Levels, varname="value", groupnames=c("Level", "variable"))
# plot
SM.lmRatio.model10.p2<-data_summary2(SM.lmRatio.model10Levels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10.p2<-data_summary2(SV.lmRatio.model10Levels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatio.model10.p1, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Mean lmRatio (Mean +/- sd)")+
theme_classic()
ggplot(SV.lmRatio.model10.p1, aes(x=Level, y=value, group = variable, color=variable))+scale_colour_viridis_d(direction=-1)+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Variance lmRatio (Mean +/- sd)")+
theme_classic()
ggplot(SM.lmRatio.model10.p2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Median lmRatio (Median +/- min/max)")+
theme_classic()
ggplot(SV.lmRatio.model10.p2, aes(x=Level, y=log(value), group = variable, color=variable))+scale_colour_viridis_d(direction=-1)+
geom_errorbar(aes(ymin=log(low), ymax=log(high)), width=.1, position=position_dodge(.3)) +
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("log Variance lmRatio (Median +/- min/max)")+
theme_classic()
… and run statistics to see the effect:
summary(aov(SM.lmRatio.model10Levels$value~SM.lmRatio.model10Levels$Level*SM.lmRatio.model10Levels$variable))
## Df Sum Sq
## SM.lmRatio.model10Levels$Level 1 1.1915
## SM.lmRatio.model10Levels$variable 6 0.0851
## SM.lmRatio.model10Levels$Level:SM.lmRatio.model10Levels$variable 6 0.0728
## Residuals 266 1.3187
## Mean Sq
## SM.lmRatio.model10Levels$Level 1.1915
## SM.lmRatio.model10Levels$variable 0.0142
## SM.lmRatio.model10Levels$Level:SM.lmRatio.model10Levels$variable 0.0121
## Residuals 0.0050
## F value Pr(>F)
## SM.lmRatio.model10Levels$Level 240.335 <2e-16
## SM.lmRatio.model10Levels$variable 2.860 0.0102
## SM.lmRatio.model10Levels$Level:SM.lmRatio.model10Levels$variable 2.448 0.0254
## Residuals
##
## SM.lmRatio.model10Levels$Level ***
## SM.lmRatio.model10Levels$variable *
## SM.lmRatio.model10Levels$Level:SM.lmRatio.model10Levels$variable *
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SM.lmRatio.model10Levels$value~SM.lmRatio.model10Levels$Level*SM.lmRatio.model10Levels$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatio.model10Levels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatio.model10Levels$Level, SM.lmRatio.model10Levels$variable
## Warning in TukeyHSD.aov(aov(SM.lmRatio.model10Levels$value ~
## SM.lmRatio.model10Levels$Level * : 'which' specified some non-factors which will
## be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SM.lmRatio.model10Levels$value ~ SM.lmRatio.model10Levels$Level * SM.lmRatio.model10Levels$variable)
##
## $`SM.lmRatio.model10Levels$variable`
## diff lwr upr p adj
## QSeq0.5-raw 1.058848e-02 -0.036188123 0.05736509 0.9939723
## QSeq1-raw 3.613214e-02 -0.010644468 0.08290874 0.2502893
## QSeq2-raw 4.398326e-02 -0.002793347 0.09075987 0.0806766
## QSeq3-raw 4.474180e-02 -0.002034802 0.09151841 0.0711136
## QSeq10-raw 4.454871e-02 -0.002227892 0.09132532 0.0734543
## QSeq100-raw 4.479576e-02 -0.001980850 0.09157236 0.0704707
## QSeq1-QSeq0.5 2.554365e-02 -0.021232951 0.07232026 0.6679591
## QSeq2-QSeq0.5 3.339478e-02 -0.013381830 0.08017138 0.3432942
## QSeq3-QSeq0.5 3.415332e-02 -0.012623285 0.08092993 0.3158560
## QSeq10-QSeq0.5 3.396023e-02 -0.012816375 0.08073684 0.3227258
## QSeq100-QSeq0.5 3.420727e-02 -0.012569333 0.08098388 0.3139508
## QSeq2-QSeq1 7.851122e-03 -0.038925484 0.05462773 0.9988588
## QSeq3-QSeq1 8.609666e-03 -0.038166940 0.05538627 0.9980786
## QSeq10-QSeq1 8.416576e-03 -0.038360030 0.05519318 0.9983087
## QSeq100-QSeq1 8.663618e-03 -0.038112988 0.05544022 0.9980101
## QSeq3-QSeq2 7.585442e-04 -0.046018062 0.04753515 1.0000000
## QSeq10-QSeq2 5.654543e-04 -0.046211152 0.04734206 1.0000000
## QSeq100-QSeq2 8.124963e-04 -0.045964110 0.04758910 1.0000000
## QSeq10-QSeq3 -1.930899e-04 -0.046969696 0.04658352 1.0000000
## QSeq100-QSeq3 5.395206e-05 -0.046722654 0.04683056 1.0000000
## QSeq100-QSeq10 2.470420e-04 -0.046529564 0.04702365 1.0000000
summary(aov(SV.lmRatio.model10Levels$value~SV.lmRatio.model10Levels$Level*SV.lmRatio.model10Levels$variable))
## Df Sum Sq
## SV.lmRatio.model10Levels$Level 1 0.1173
## SV.lmRatio.model10Levels$variable 6 0.1450
## SV.lmRatio.model10Levels$Level:SV.lmRatio.model10Levels$variable 6 0.0072
## Residuals 266 0.8183
## Mean Sq
## SV.lmRatio.model10Levels$Level 0.11726
## SV.lmRatio.model10Levels$variable 0.02416
## SV.lmRatio.model10Levels$Level:SV.lmRatio.model10Levels$variable 0.00120
## Residuals 0.00308
## F value
## SV.lmRatio.model10Levels$Level 38.117
## SV.lmRatio.model10Levels$variable 7.853
## SV.lmRatio.model10Levels$Level:SV.lmRatio.model10Levels$variable 0.389
## Residuals
## Pr(>F)
## SV.lmRatio.model10Levels$Level 2.48e-09 ***
## SV.lmRatio.model10Levels$variable 8.46e-08 ***
## SV.lmRatio.model10Levels$Level:SV.lmRatio.model10Levels$variable 0.886
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SV.lmRatio.model10Levels$value~SV.lmRatio.model10Levels$Level*SV.lmRatio.model10Levels$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatio.model10Levels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatio.model10Levels$Level, SV.lmRatio.model10Levels$variable
## Warning in TukeyHSD.aov(aov(SV.lmRatio.model10Levels$value ~
## SV.lmRatio.model10Levels$Level * : 'which' specified some non-factors which will
## be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SV.lmRatio.model10Levels$value ~ SV.lmRatio.model10Levels$Level * SV.lmRatio.model10Levels$variable)
##
## $`SV.lmRatio.model10Levels$variable`
## diff lwr upr p adj
## QSeq0.5-raw 0.0430083257 0.006160901 0.079855750 0.0108173
## QSeq1-raw 0.0008151688 -0.036032255 0.037662593 1.0000000
## QSeq2-raw -0.0219323982 -0.058779822 0.014915026 0.5705761
## QSeq3-raw -0.0192015612 -0.056048986 0.017645863 0.7152416
## QSeq10-raw -0.0248086389 -0.061656063 0.012038785 0.4168778
## QSeq100-raw -0.0250136742 -0.061861098 0.011833750 0.4064418
## QSeq1-QSeq0.5 -0.0421931569 -0.079040581 -0.005345733 0.0134514
## QSeq2-QSeq0.5 -0.0649407239 -0.101788148 -0.028093300 0.0000069
## QSeq3-QSeq0.5 -0.0622098869 -0.099057311 -0.025362463 0.0000198
## QSeq10-QSeq0.5 -0.0678169646 -0.104664389 -0.030969540 0.0000022
## QSeq100-QSeq0.5 -0.0680219999 -0.104869424 -0.031174576 0.0000020
## QSeq2-QSeq1 -0.0227475670 -0.059594991 0.014099857 0.5261768
## QSeq3-QSeq1 -0.0200167300 -0.056864154 0.016830694 0.6734489
## QSeq10-QSeq1 -0.0256238077 -0.062471232 0.011223617 0.3760302
## QSeq100-QSeq1 -0.0258288430 -0.062676267 0.011018581 0.3660443
## QSeq3-QSeq2 0.0027308369 -0.034116587 0.039578261 0.9999904
## QSeq10-QSeq2 -0.0028762408 -0.039723665 0.033971184 0.9999869
## QSeq100-QSeq2 -0.0030812760 -0.039928700 0.033766148 0.9999803
## QSeq10-QSeq3 -0.0056070777 -0.042454502 0.031240347 0.9993478
## QSeq100-QSeq3 -0.0058121130 -0.042659537 0.031035311 0.9991989
## QSeq100-QSeq10 -0.0002050353 -0.037052460 0.036642389 1.0000000
Conclusion: there is an interaction between the normalization method and the internal structure of the community on our ability to accurately describe the relationship between taxa and the environmental gradients. According to this analysis we should prefer QSeq3,10 and 100.
What about our ability to detect the experimental design? Following the same methodology:
Summarize.lmRatiotabModel.Median<-function(trt, method){
Ftab<-matrix(NA, nrow = length(trt), ncol = length(method)) # make matrix
for(i in 1:length(trt)){
for(j in 1:length(method)){
Ftab[i,j]<-median(trt[[i]][[method[j]]]$lmRatiotab.model, na.rm=T)
#print(sum(trt[[i]][j]$PERMANOVA$aov.tab$F.Model))
}
}
rownames(Ftab)<-names(trt)
colnames(Ftab)<-method
Ftab
}
Summarize.lmRatiotabModel.Var<-function(trt, method){
Ftab<-matrix(NA, nrow = length(trt), ncol = length(method)) # make matrix
for(i in 1:length(trt)){
for(j in 1:length(method)){
Ftab[i,j]<-var(trt[[i]][[method[j]]]$lmRatiotab.model, na.rm=T)
#print(sum(trt[[i]][j]$PERMANOVA$aov.tab$F.Model))
}
}
rownames(Ftab)<-names(trt)
colnames(Ftab)<-method
Ftab
}
SM.lmRatioM.model10.A<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.A,method2))
SV.lmRatioM.model10.A<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.A,method2))
SM.lmRatioM.model10.B<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.B,method2))
SV.lmRatioM.model10.B<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.B,method2))
SM.lmRatioM.model10.C<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C,method2))
SV.lmRatioM.model10.C<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C,method2))
SM.lmRatioM.model10.D<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.D,method2))
SV.lmRatioM.model10.D<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.D,method2))
# prepare data for merging datasets
SM.lmRatioM.model10.A$Level<-c(rep(1,10))
SV.lmRatioM.model10.A$Level<-c(rep(1,10))
SM.lmRatioM.model10.B$Level<-c(rep(2,10))
SV.lmRatioM.model10.B$Level<-c(rep(2,10))
SM.lmRatioM.model10.C$Level<-c(rep(3,10))
SV.lmRatioM.model10.C$Level<-c(rep(3,10))
SM.lmRatioM.model10.D$Level<-c(rep(4,10))
SV.lmRatioM.model10.D$Level<-c(rep(4,10))
SM.lmRatioM.model10.A<-melt(SM.lmRatioM.model10.A, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.A<-melt(SV.lmRatioM.model10.A, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.B<-melt(SM.lmRatioM.model10.B, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.B<-melt(SV.lmRatioM.model10.B, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.C<-melt(SM.lmRatioM.model10.C, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C<-melt(SV.lmRatioM.model10.C, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.D<-melt(SM.lmRatioM.model10.D, id.vars = "Level", measure.vars = method)
SV.lmRatioM.model10.D<-melt(SV.lmRatioM.model10.D, id.vars = "Level", measure.vars = method2)
# merge datasets
SM.lmRatioM.model10Levels<-do.call("rbind", list(SM.lmRatioM.model10.A,SM.lmRatioM.model10.B,SM.lmRatioM.model10.C,SM.lmRatioM.model10.D))
SV.lmRatioM.model10Levels<-do.call("rbind", list(SV.lmRatioM.model10.A,SV.lmRatioM.model10.B,SV.lmRatioM.model10.C,SV.lmRatioM.model10.D))
# summarize for plotting
SM.lmRatioM.model10.p1<-data_summary(SM.lmRatioM.model10Levels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatioM.model10.p1<-data_summary(SV.lmRatioM.model10Levels, varname="value", groupnames=c("Level", "variable"))
SM.lmRatioM.model10.p2<-data_summary2(SM.lmRatioM.model10Levels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatioM.model10.p2<-data_summary2(SV.lmRatioM.model10Levels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatioM.model10.p1, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d()+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Median lmRatio.model (Mean +/- sd)")+
theme_classic()
ggplot(SV.lmRatioM.model10.p1, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Variance lmRatio.model (Mean +/- sd)")+
theme_classic()
ggplot(SM.lmRatioM.model10.p2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d()+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Median lmRatio.model (Median +/- min/max)")+
theme_classic()
ggplot(SV.lmRatioM.model10.p2, aes(x=Level, y=log(value), group = variable, color=variable))+
geom_errorbar(aes(ymin=log(low), ymax=log(high)), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Variance lmRatio.model (Median +/- min/max)")+
theme_classic()
And again we do the stats:
summary(aov(SM.lmRatioM.model10Levels$value~SM.lmRatioM.model10Levels$Level*SM.lmRatioM.model10Levels$variable))
## Df Sum Sq
## SM.lmRatioM.model10Levels$Level 1 0.8811
## SM.lmRatioM.model10Levels$variable 6 0.0465
## SM.lmRatioM.model10Levels$Level:SM.lmRatioM.model10Levels$variable 6 0.0472
## Residuals 256 1.2936
## Mean Sq
## SM.lmRatioM.model10Levels$Level 0.8811
## SM.lmRatioM.model10Levels$variable 0.0078
## SM.lmRatioM.model10Levels$Level:SM.lmRatioM.model10Levels$variable 0.0079
## Residuals 0.0051
## F value
## SM.lmRatioM.model10Levels$Level 174.365
## SM.lmRatioM.model10Levels$variable 1.534
## SM.lmRatioM.model10Levels$Level:SM.lmRatioM.model10Levels$variable 1.556
## Residuals
## Pr(>F)
## SM.lmRatioM.model10Levels$Level <2e-16 ***
## SM.lmRatioM.model10Levels$variable 0.167
## SM.lmRatioM.model10Levels$Level:SM.lmRatioM.model10Levels$variable 0.161
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SM.lmRatioM.model10Levels$value~SM.lmRatioM.model10Levels$variable)) # something wrong here?
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SM.lmRatioM.model10Levels$value ~ SM.lmRatioM.model10Levels$variable)
##
## $`SM.lmRatioM.model10Levels$variable`
## diff lwr upr p adj
## QSeq0.5-raw -0.0056695427 -0.07139375 0.06005466 0.9999763
## QSeq1-raw 0.0230401489 -0.04268406 0.08876435 0.9438091
## QSeq2-raw 0.0323009994 -0.03342321 0.09802521 0.7679967
## QSeq3-raw 0.0316789184 -0.03404529 0.09740312 0.7839327
## QSeq10-raw 0.0330173453 -0.03270686 0.09874155 0.7490568
## QSeq100-raw 0.0325037550 -0.03322045 0.09822796 0.7626979
## QSeq1-QSeq0.5 0.0287096916 -0.03213910 0.08955848 0.8004986
## QSeq2-QSeq0.5 0.0379705421 -0.02287825 0.09881933 0.5127573
## QSeq3-QSeq0.5 0.0373484612 -0.02350033 0.09819725 0.5332020
## QSeq10-QSeq0.5 0.0386868880 -0.02216190 0.09953568 0.4893693
## QSeq100-QSeq0.5 0.0381732977 -0.02267549 0.09902209 0.5061178
## QSeq2-QSeq1 0.0092608505 -0.05158794 0.07010964 0.9993468
## QSeq3-QSeq1 0.0086387695 -0.05221002 0.06948756 0.9995621
## QSeq10-QSeq1 0.0099771964 -0.05087159 0.07082599 0.9990000
## QSeq100-QSeq1 0.0094636061 -0.05138518 0.07031240 0.9992605
## QSeq3-QSeq2 -0.0006220810 -0.06147087 0.06022671 1.0000000
## QSeq10-QSeq2 0.0007163459 -0.06013245 0.06156514 1.0000000
## QSeq100-QSeq2 0.0002027556 -0.06064604 0.06105155 1.0000000
## QSeq10-QSeq3 0.0013384269 -0.05951036 0.06218722 1.0000000
## QSeq100-QSeq3 0.0008248366 -0.06002395 0.06167363 1.0000000
## QSeq100-QSeq10 -0.0005135903 -0.06136238 0.06033520 1.0000000
summary(aov(SV.lmRatioM.model10Levels$value~SV.lmRatioM.model10Levels$Level*SV.lmRatioM.model10Levels$variable))
## Df Sum Sq
## SV.lmRatioM.model10Levels$Level 1 0.0564
## SV.lmRatioM.model10Levels$variable 6 0.7198
## SV.lmRatioM.model10Levels$Level:SV.lmRatioM.model10Levels$variable 6 0.2731
## Residuals 266 2.5158
## Mean Sq
## SV.lmRatioM.model10Levels$Level 0.05645
## SV.lmRatioM.model10Levels$variable 0.11997
## SV.lmRatioM.model10Levels$Level:SV.lmRatioM.model10Levels$variable 0.04551
## Residuals 0.00946
## F value
## SV.lmRatioM.model10Levels$Level 5.968
## SV.lmRatioM.model10Levels$variable 12.685
## SV.lmRatioM.model10Levels$Level:SV.lmRatioM.model10Levels$variable 4.812
## Residuals
## Pr(>F)
## SV.lmRatioM.model10Levels$Level 0.015217 *
## SV.lmRatioM.model10Levels$variable 1.38e-12 ***
## SV.lmRatioM.model10Levels$Level:SV.lmRatioM.model10Levels$variable 0.000111 ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SV.lmRatioM.model10Levels$value~SV.lmRatioM.model10Levels$Level*SV.lmRatioM.model10Levels$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatioM.model10Levels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatioM.model10Levels$Level, SV.lmRatioM.model10Levels$variable
## Warning in TukeyHSD.aov(aov(SV.lmRatioM.model10Levels$value ~
## SV.lmRatioM.model10Levels$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SV.lmRatioM.model10Levels$value ~ SV.lmRatioM.model10Levels$Level * SV.lmRatioM.model10Levels$variable)
##
## $`SV.lmRatioM.model10Levels$variable`
## diff lwr upr p adj
## QSeq0.5-raw -0.0632370521 -0.12784662 0.001372512 0.0595331
## QSeq1-raw -0.1113114603 -0.17592102 -0.046701896 0.0000122
## QSeq2-raw -0.1338000916 -0.19840966 -0.069190527 0.0000001
## QSeq3-raw -0.1392924063 -0.20390197 -0.074682842 0.0000000
## QSeq10-raw -0.1447583441 -0.20936791 -0.080148780 0.0000000
## QSeq100-raw -0.1450190766 -0.20962864 -0.080409512 0.0000000
## QSeq1-QSeq0.5 -0.0480744082 -0.11268397 0.016535156 0.2932610
## QSeq2-QSeq0.5 -0.0705630395 -0.13517260 -0.005953475 0.0222406
## QSeq3-QSeq0.5 -0.0760553542 -0.14066492 -0.011445790 0.0097927
## QSeq10-QSeq0.5 -0.0815212920 -0.14613086 -0.016911728 0.0040553
## QSeq100-QSeq0.5 -0.0817820245 -0.14639159 -0.017172460 0.0038822
## QSeq2-QSeq1 -0.0224886313 -0.08709820 0.042120933 0.9456854
## QSeq3-QSeq1 -0.0279809460 -0.09259051 0.036628618 0.8576276
## QSeq10-QSeq1 -0.0334468838 -0.09805645 0.031162680 0.7215635
## QSeq100-QSeq1 -0.0337076163 -0.09831718 0.030901948 0.7141271
## QSeq3-QSeq2 -0.0054923147 -0.07010188 0.059117249 0.9999783
## QSeq10-QSeq2 -0.0109582525 -0.07556782 0.053651312 0.9987890
## QSeq100-QSeq2 -0.0112189850 -0.07582855 0.053390579 0.9986164
## QSeq10-QSeq3 -0.0054659378 -0.07007550 0.059143626 0.9999789
## QSeq100-QSeq3 -0.0057266703 -0.07033623 0.058882894 0.9999722
## QSeq100-QSeq10 -0.0002607325 -0.06487030 0.064348832 1.0000000
An emerging pattern that we see here is that raw data without any processing generally performs worst when there is less structure and environmental variables can act more as a filter. Also, in our normalization method QSeq, higher sampling variables that don’t omit low abundance taxa perform better. Higher abundance will continue to perform even better.
Let’s check the accuracy of the model:
# outputs an object with both variance and median
TaxRatio.model10.A<-getTaxCor.Tab(model10.A,method2)
TaxRatio.model10.B<-getTaxCor.Tab(model10.B,method2)
TaxRatio.model10.C<-getTaxCor.Tab(model10.C,method2)
TaxRatio.model10.D<-getTaxCor.Tab(model10.D,method2)
#separate median and variance tables, and melt
V.TaxRatio.model10.A<-melt(TaxRatio.model10.A$V.tax)
M.TaxRatio.model10.A<-melt(TaxRatio.model10.A$Median.tax)
V.TaxRatio.model10.B<-melt(TaxRatio.model10.B$V.tax)
M.TaxRatio.model10.B<-melt(TaxRatio.model10.B$Median.tax)
V.TaxRatio.model10.C<-melt(TaxRatio.model10.C$V.tax)
M.TaxRatio.model10.C<-melt(TaxRatio.model10.C$Median.tax)
V.TaxRatio.model10.D<-melt(TaxRatio.model10.D$V.tax)
M.TaxRatio.model10.D<-melt(TaxRatio.model10.D$Median.tax)
# prepare data for merging datasets
V.TaxRatio.model10.A<-as.data.frame(V.TaxRatio.model10.A)
M.TaxRatio.model10.A<-as.data.frame(M.TaxRatio.model10.A)
V.TaxRatio.model10.B<-as.data.frame(V.TaxRatio.model10.B)
M.TaxRatio.model10.B<-as.data.frame(M.TaxRatio.model10.B)
V.TaxRatio.model10.C<-as.data.frame(V.TaxRatio.model10.C)
M.TaxRatio.model10.C<-as.data.frame(M.TaxRatio.model10.C)
V.TaxRatio.model10.D<-as.data.frame(V.TaxRatio.model10.D)
M.TaxRatio.model10.D<-as.data.frame(M.TaxRatio.model10.D)
V.TaxRatio.model10.A$Level<-c(rep(1,nrow(V.TaxRatio.model10.A)))
V.TaxRatio.model10.B$Level<-c(rep(2,nrow(V.TaxRatio.model10.B)))
V.TaxRatio.model10.C$Level<-c(rep(3,nrow(V.TaxRatio.model10.C)))
V.TaxRatio.model10.D$Level<-c(rep(4,nrow(V.TaxRatio.model10.D)))
M.TaxRatio.model10.A$Level<-c(rep(1,nrow(M.TaxRatio.model10.A)))
M.TaxRatio.model10.B$Level<-c(rep(2,nrow(M.TaxRatio.model10.B)))
M.TaxRatio.model10.C$Level<-c(rep(3,nrow(M.TaxRatio.model10.C)))
M.TaxRatio.model10.D$Level<-c(rep(4,nrow(M.TaxRatio.model10.D)))
# merge datasets
V.TaxRatio.model10Levels<-do.call("rbind", list(V.TaxRatio.model10.A,V.TaxRatio.model10.B,V.TaxRatio.model10.C,V.TaxRatio.model10.D))
M.TaxRatio.model10Levels<-do.call("rbind", list(M.TaxRatio.model10.A,M.TaxRatio.model10.B,M.TaxRatio.model10.C,M.TaxRatio.model10.D))
# summarize for plotting
V.TaxRatio.model10.p1<-data_summary(V.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.p1<-data_summary(M.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
V.TaxRatio.model10.p2<-data_summary2(V.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.p2<-data_summary2(M.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
# plot
ggplot(V.TaxRatio.model10.p1, aes(x=Level, y=value, group = Var2, color=Var2))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Variance taxRatio (Mean +/- sd)")+
theme_classic()
ggplot(M.TaxRatio.model10.p1, aes(x=Level, y=value, group = Var2, color=Var2))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Mean taxRatio (Mean +/- sd)")+
theme_classic()
ggplot(V.TaxRatio.model10.p2, aes(x=Level, y=log10(value), group = Var2, color=Var2))+
geom_errorbar(aes(ymin=log10(low), ymax=log10(high)), width=.1, position=position_dodge(.3)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Variance taxRatio (Median +/- min/max)")+
theme_classic()
ggplot(M.TaxRatio.model10.p2, aes(x=Level, y=value, group = Var2, color=Var2))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("log Median taxRatio (Median +/- min/max)")+
theme_classic()
Note: In general, the results of this portion of the simulation show that QSeq0.5 underperforms compared to all other QSeq methods; that QSeq methods generally are better at estimating the mean value than un-normalized (have less systemic under or over estimation), but that often at lower degrees of structure the un-normalized dataset has less variance around the mean. But, this portion of the simulation tends to be less stable, and occasionally fails to produce a significant result. Therefore I will give guidelines on how to interpret the outputs, but not discuss specific conclusions.
Generally variance should approach zero, and the mean should approach 1. The greater the deviation of the variance from zero (and the greater the range in variance values), the less accuracy on a taxon-by-taxon basis in estimating relationships among taxa. The farther the mean deviates from 1, the greater the systemic bias (over or underestimation) of the strength of the relationship. Let’s check the stats:
summary(aov(M.TaxRatio.model10Levels$value~M.TaxRatio.model10Levels$Level*M.TaxRatio.model10Levels$Var2))
## Df Sum Sq Mean Sq
## M.TaxRatio.model10Levels$Level 1 74.3 74.31
## M.TaxRatio.model10Levels$Var2 6 2.6 0.43
## M.TaxRatio.model10Levels$Level:M.TaxRatio.model10Levels$Var2 6 14.4 2.40
## Residuals 266 530.9 2.00
## F value Pr(>F)
## M.TaxRatio.model10Levels$Level 37.234 3.69e-09
## M.TaxRatio.model10Levels$Var2 0.215 0.972
## M.TaxRatio.model10Levels$Level:M.TaxRatio.model10Levels$Var2 1.200 0.306
## Residuals
##
## M.TaxRatio.model10Levels$Level ***
## M.TaxRatio.model10Levels$Var2
## M.TaxRatio.model10Levels$Level:M.TaxRatio.model10Levels$Var2
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(M.TaxRatio.model10Levels$value~M.TaxRatio.model10Levels$Var2))
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = M.TaxRatio.model10Levels$value ~ M.TaxRatio.model10Levels$Var2)
##
## $`M.TaxRatio.model10Levels$Var2`
## diff lwr upr p adj
## QSeq0.5-raw 0.187238522 -0.8133721 1.1878491 0.9978954
## QSeq1-raw -0.114817833 -1.1154285 0.8857928 0.9998732
## QSeq2-raw -0.083411588 -1.0840222 0.9171990 0.9999807
## QSeq3-raw -0.084835496 -1.0854461 0.9157751 0.9999787
## QSeq10-raw -0.068804869 -1.0694155 0.9318058 0.9999938
## QSeq100-raw -0.071544944 -1.0721556 0.9290657 0.9999922
## QSeq1-QSeq0.5 -0.302056355 -1.3026670 0.6985543 0.9728482
## QSeq2-QSeq0.5 -0.270650110 -1.2712607 0.7299605 0.9844919
## QSeq3-QSeq0.5 -0.272074018 -1.2726846 0.7285366 0.9840640
## QSeq10-QSeq0.5 -0.256043391 -1.2566540 0.7445672 0.9883996
## QSeq100-QSeq0.5 -0.258783465 -1.2593941 0.7418272 0.9877309
## QSeq2-QSeq1 0.031406245 -0.9692044 1.0320169 0.9999999
## QSeq3-QSeq1 0.029982337 -0.9706283 1.0305930 1.0000000
## QSeq10-QSeq1 0.046012965 -0.9545977 1.0466236 0.9999994
## QSeq100-QSeq1 0.043272890 -0.9573377 1.0438835 0.9999996
## QSeq3-QSeq2 -0.001423908 -1.0020345 0.9991867 1.0000000
## QSeq10-QSeq2 0.014606720 -0.9860039 1.0152173 1.0000000
## QSeq100-QSeq2 0.011866645 -0.9887440 1.0124773 1.0000000
## QSeq10-QSeq3 0.016030627 -0.9845800 1.0166413 1.0000000
## QSeq100-QSeq3 0.013290552 -0.9873201 1.0139012 1.0000000
## QSeq100-QSeq10 -0.002740075 -1.0033507 0.9978705 1.0000000
summary(aov(V.TaxRatio.model10Levels$value~V.TaxRatio.model10Levels$Level*V.TaxRatio.model10Levels$Var2))
## Df Sum Sq
## V.TaxRatio.model10Levels$Level 1 7.312e+09
## V.TaxRatio.model10Levels$Var2 6 8.470e+08
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2 6 1.061e+09
## Residuals 266 1.179e+11
## Mean Sq F value
## V.TaxRatio.model10Levels$Level 7.312e+09 16.495
## V.TaxRatio.model10Levels$Var2 1.412e+08 0.318
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2 1.768e+08 0.399
## Residuals 4.433e+08
## Pr(>F)
## V.TaxRatio.model10Levels$Level 6.42e-05 ***
## V.TaxRatio.model10Levels$Var2 0.927
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2 0.879
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(V.TaxRatio.model10Levels$value~V.TaxRatio.model10Levels$Level*V.TaxRatio.model10Levels$Var2))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10Levels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10Levels$Level, V.TaxRatio.model10Levels$Var2
## Warning in TukeyHSD.aov(aov(V.TaxRatio.model10Levels$value ~
## V.TaxRatio.model10Levels$Level * : 'which' specified some non-factors which will
## be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = V.TaxRatio.model10Levels$value ~ V.TaxRatio.model10Levels$Level * V.TaxRatio.model10Levels$Var2)
##
## $`V.TaxRatio.model10Levels$Var2`
## diff lwr upr p adj
## QSeq0.5-raw -6189.17356 -20176.266 7797.919 0.8446855
## QSeq1-raw -2208.53837 -16195.630 11778.554 0.9991942
## QSeq2-raw -1986.39590 -15973.488 12000.696 0.9995616
## QSeq3-raw -1774.36718 -15761.459 12212.725 0.9997720
## QSeq10-raw -1873.42510 -15860.517 12113.667 0.9996875
## QSeq100-raw -1850.20400 -15837.296 12136.888 0.9997093
## QSeq1-QSeq0.5 3980.63519 -10006.457 17967.727 0.9798212
## QSeq2-QSeq0.5 4202.77766 -9784.314 18189.870 0.9734370
## QSeq3-QSeq0.5 4414.80638 -9572.286 18401.898 0.9660820
## QSeq10-QSeq0.5 4315.74846 -9671.344 18302.841 0.9696793
## QSeq100-QSeq0.5 4338.96956 -9648.123 18326.062 0.9688618
## QSeq2-QSeq1 222.14247 -13764.950 14209.235 1.0000000
## QSeq3-QSeq1 434.17119 -13552.921 14421.263 0.9999999
## QSeq10-QSeq1 335.11326 -13651.979 14322.205 1.0000000
## QSeq100-QSeq1 358.33437 -13628.758 14345.426 1.0000000
## QSeq3-QSeq2 212.02872 -13775.063 14199.121 1.0000000
## QSeq10-QSeq2 112.97080 -13874.121 14100.063 1.0000000
## QSeq100-QSeq2 136.19190 -13850.900 14123.284 1.0000000
## QSeq10-QSeq3 -99.05792 -14086.150 13888.034 1.0000000
## QSeq100-QSeq3 -75.83682 -14062.929 13911.255 1.0000000
## QSeq100-QSeq10 23.22111 -13963.871 14010.313 1.0000000
#leveneTest(value~as.factor(Level), data=V.TaxRatio.model10.p)
Now let’s look at a common community level statistic. PERMANOVA outputs:
# get permanova geography ####
model10A.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A,method2, "CategoryRratio"))
model10A.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F1Rratio"))
model10A.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F2Rratio"))
model10A.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F3Rratio"))
model10A.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F4Rratio"))
model10A.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A,method2, "F5Rratio"))
model10B.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "CategoryRratio"))
model10B.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "F1Rratio"))
model10B.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "F2Rratio"))
model10B.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "F3Rratio"))
model10B.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "F4Rratio"))
model10B.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "F5Rratio"))
model10C.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "CategoryRratio"))
model10C.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "F1Rratio"))
model10C.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "F2Rratio"))
model10C.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "F3Rratio"))
model10C.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "F4Rratio"))
model10C.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "F5Rratio"))
model10D.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "CategoryRratio"))
model10D.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "F1Rratio"))
model10D.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "F2Rratio"))
model10D.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "F3Rratio"))
model10D.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "F4Rratio"))
model10D.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "F5Rratio"))
model10A.Permanova.model$Level<-c(rep(1,10))
model10A.Permanova.env1$Level<-c(rep(1,10))
model10A.Permanova.env2$Level<-c(rep(1,10))
model10A.Permanova.env3$Level<-c(rep(1,10))
model10A.Permanova.env4$Level<-c(rep(1,10))
model10A.Permanova.env5$Level<-c(rep(1,10))
model10B.Permanova.model$Level<-c(rep(2,10))
model10B.Permanova.env1$Level<-c(rep(2,10))
model10B.Permanova.env2$Level<-c(rep(2,10))
model10B.Permanova.env3$Level<-c(rep(2,10))
model10B.Permanova.env4$Level<-c(rep(2,10))
model10B.Permanova.env5$Level<-c(rep(2,10))
model10C.Permanova.model$Level<-c(rep(3,10))
model10C.Permanova.env1$Level<-c(rep(3,10))
model10C.Permanova.env2$Level<-c(rep(3,10))
model10C.Permanova.env3$Level<-c(rep(3,10))
model10C.Permanova.env4$Level<-c(rep(3,10))
model10C.Permanova.env5$Level<-c(rep(3,10))
model10D.Permanova.model$Level<-c(rep(4,10))
model10D.Permanova.env1$Level<-c(rep(4,10))
model10D.Permanova.env2$Level<-c(rep(4,10))
model10D.Permanova.env3$Level<-c(rep(4,10))
model10D.Permanova.env4$Level<-c(rep(4,10))
model10D.Permanova.env5$Level<-c(rep(4,10))
permanova.model10Levels.model<-do.call("rbind", list(model10A.Permanova.model,model10B.Permanova.model,model10C.Permanova.model,model10D.Permanova.model))
permanova.model10Levels.env1<-do.call("rbind", list(model10A.Permanova.env1,model10B.Permanova.env1,model10C.Permanova.env1,model10D.Permanova.env1))
permanova.model10Levels.env2<-do.call("rbind", list(model10A.Permanova.env2,model10B.Permanova.env2,model10C.Permanova.env2,model10D.Permanova.env2))
permanova.model10Levels.env3<-do.call("rbind", list(model10A.Permanova.env3,model10B.Permanova.env3,model10C.Permanova.env3,model10D.Permanova.env3))
permanova.model10Levels.env4<-do.call("rbind", list(model10A.Permanova.env4,model10B.Permanova.env4,model10C.Permanova.env4,model10D.Permanova.env4))
permanova.model10Levels.env5<-do.call("rbind", list(model10A.Permanova.env5,model10B.Permanova.env5,model10C.Permanova.env5,model10D.Permanova.env5))
permanova.model10Levels.model<-melt(permanova.model10Levels.model, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.env1<-melt(permanova.model10Levels.env1, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.env2<-melt(permanova.model10Levels.env2, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.env3<-melt(permanova.model10Levels.env3, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.env4<-melt(permanova.model10Levels.env4, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.env5<-melt(permanova.model10Levels.env5, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.modelP<-data_summary2(permanova.model10Levels.model, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env1P<-data_summary2(permanova.model10Levels.env1, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env2P<-data_summary2(permanova.model10Levels.env2, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env3P<-data_summary2(permanova.model10Levels.env3, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env4P<-data_summary2(permanova.model10Levels.env4, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env5P<-data_summary2(permanova.model10Levels.env5, varname="value", groupnames=c("Level", "variable"))
ggplot(permanova.model10Levels.modelP, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova modelRatio (Median +/- min/max)")+
theme_classic()
ggplot(permanova.model10Levels.env1P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova env1Ratio (Median +/- min/max)")+
theme_classic()
ggplot(permanova.model10Levels.env2P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova env2Ratio (Median +/- min/max)")+
theme_classic()
ggplot(permanova.model10Levels.env3P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova env3Ratio (Median +/- min/max)")+
theme_classic()
ggplot(permanova.model10Levels.env4P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova env4Ratio (Median +/- min/max)")+
theme_classic()
ggplot(permanova.model10Levels.env5P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova env5Ratio (Median +/- min/max)")+
theme_classic()
permanova.model10Levels.modelP1<-data_summary(permanova.model10Levels.model, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env1P1<-data_summary(permanova.model10Levels.env1, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env2P1<-data_summary(permanova.model10Levels.env2, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env3P1<-data_summary(permanova.model10Levels.env3, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env4P1<-data_summary(permanova.model10Levels.env4, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env5P1<-data_summary(permanova.model10Levels.env5, varname="value", groupnames=c("Level", "variable"))
ggplot(permanova.model10Levels.modelP1, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova modelRatio (Mean +/- sd)")+
theme_classic()
ggplot(permanova.model10Levels.env1P1, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova env1Ratio (Mean +/- sd)")+
theme_classic()
ggplot(permanova.model10Levels.env2P1, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova env2Ratio (Mean +/- sd)")+
theme_classic()
ggplot(permanova.model10Levels.env3P1, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova env3Ratio (Mean +/- sd)")+
theme_classic()
ggplot(permanova.model10Levels.env4P1, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova env4Ratio (Mean +/- sd)")+
theme_classic()
ggplot(permanova.model10Levels.env5P1, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.3))+
geom_point(position=position_dodge(.3))+
xlab("Degree of Structure")+
ylab("Permanova env5Ratio (Mean +/- sd)")+
theme_classic()
PERMANOVA results are very consistent: the statistical model is typically captured equally well across normalization methods. However, QSeq methods significantly increase the accuracy of relating specific environmental gradients to the community structure.
Statistics:
summary(aov(permanova.model10Levels.model$value~permanova.model10Levels.model$Level*permanova.model10Levels.model$variable))
## Df
## permanova.model10Levels.model$Level 1
## permanova.model10Levels.model$variable 6
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable 6
## Residuals 266
## Sum Sq
## permanova.model10Levels.model$Level 0.03567
## permanova.model10Levels.model$variable 0.00002
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable 0.00011
## Residuals 0.07067
## Mean Sq
## permanova.model10Levels.model$Level 0.03567
## permanova.model10Levels.model$variable 0.00000
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable 0.00002
## Residuals 0.00027
## F value
## permanova.model10Levels.model$Level 134.269
## permanova.model10Levels.model$variable 0.010
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable 0.068
## Residuals
## Pr(>F)
## permanova.model10Levels.model$Level <2e-16
## permanova.model10Levels.model$variable 1.000
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable 0.999
## Residuals
##
## permanova.model10Levels.model$Level ***
## permanova.model10Levels.model$variable
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(permanova.model10Levels.env1$value~permanova.model10Levels.env1$Level*permanova.model10Levels.env1$variable))
## Df
## permanova.model10Levels.env1$Level 1
## permanova.model10Levels.env1$variable 6
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable 6
## Residuals 266
## Sum Sq
## permanova.model10Levels.env1$Level 0.0147
## permanova.model10Levels.env1$variable 0.1168
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable 0.0216
## Residuals 2.5369
## Mean Sq
## permanova.model10Levels.env1$Level 0.014673
## permanova.model10Levels.env1$variable 0.019473
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable 0.003593
## Residuals 0.009537
## F value
## permanova.model10Levels.env1$Level 1.538
## permanova.model10Levels.env1$variable 2.042
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable 0.377
## Residuals
## Pr(>F)
## permanova.model10Levels.env1$Level 0.2159
## permanova.model10Levels.env1$variable 0.0605
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable 0.8935
## Residuals
##
## permanova.model10Levels.env1$Level
## permanova.model10Levels.env1$variable .
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(permanova.model10Levels.env2$value~permanova.model10Levels.env2$Level*permanova.model10Levels.env2$variable))
## Df
## permanova.model10Levels.env2$Level 1
## permanova.model10Levels.env2$variable 6
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable 6
## Residuals 266
## Sum Sq
## permanova.model10Levels.env2$Level 0.2725
## permanova.model10Levels.env2$variable 2.4442
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable 0.9495
## Residuals 1.3632
## Mean Sq
## permanova.model10Levels.env2$Level 0.2725
## permanova.model10Levels.env2$variable 0.4074
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable 0.1582
## Residuals 0.0051
## F value
## permanova.model10Levels.env2$Level 53.16
## permanova.model10Levels.env2$variable 79.49
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable 30.88
## Residuals
## Pr(>F)
## permanova.model10Levels.env2$Level 3.51e-12
## permanova.model10Levels.env2$variable < 2e-16
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable < 2e-16
## Residuals
##
## permanova.model10Levels.env2$Level ***
## permanova.model10Levels.env2$variable ***
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(permanova.model10Levels.env3$value~permanova.model10Levels.env3$Level*permanova.model10Levels.env3$variable))
## Df
## permanova.model10Levels.env3$Level 1
## permanova.model10Levels.env3$variable 6
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable 6
## Residuals 266
## Sum Sq
## permanova.model10Levels.env3$Level 0.2745
## permanova.model10Levels.env3$variable 1.2035
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable 0.1164
## Residuals 1.2358
## Mean Sq
## permanova.model10Levels.env3$Level 0.27454
## permanova.model10Levels.env3$variable 0.20058
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable 0.01940
## Residuals 0.00465
## F value
## permanova.model10Levels.env3$Level 59.094
## permanova.model10Levels.env3$variable 43.175
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable 4.176
## Residuals
## Pr(>F)
## permanova.model10Levels.env3$Level 2.91e-13
## permanova.model10Levels.env3$variable < 2e-16
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable 0.000496
## Residuals
##
## permanova.model10Levels.env3$Level ***
## permanova.model10Levels.env3$variable ***
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(permanova.model10Levels.env4$value~permanova.model10Levels.env4$Level*permanova.model10Levels.env4$variable))
## Df
## permanova.model10Levels.env4$Level 1
## permanova.model10Levels.env4$variable 6
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable 6
## Residuals 266
## Sum Sq
## permanova.model10Levels.env4$Level 0.200
## permanova.model10Levels.env4$variable 0.309
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable 0.067
## Residuals 6.642
## Mean Sq
## permanova.model10Levels.env4$Level 0.20019
## permanova.model10Levels.env4$variable 0.05156
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable 0.01114
## Residuals 0.02497
## F value
## permanova.model10Levels.env4$Level 8.017
## permanova.model10Levels.env4$variable 2.065
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable 0.446
## Residuals
## Pr(>F)
## permanova.model10Levels.env4$Level 0.00499
## permanova.model10Levels.env4$variable 0.05764
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable 0.84738
## Residuals
##
## permanova.model10Levels.env4$Level **
## permanova.model10Levels.env4$variable .
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(permanova.model10Levels.env5$value~permanova.model10Levels.env5$Level*permanova.model10Levels.env5$variable))
## Df
## permanova.model10Levels.env5$Level 1
## permanova.model10Levels.env5$variable 6
## permanova.model10Levels.env5$Level:permanova.model10Levels.env5$variable 6
## Residuals 266
## Sum Sq
## permanova.model10Levels.env5$Level 0.000
## permanova.model10Levels.env5$variable 0.889
## permanova.model10Levels.env5$Level:permanova.model10Levels.env5$variable 0.412
## Residuals 31.097
## Mean Sq
## permanova.model10Levels.env5$Level 0.00006
## permanova.model10Levels.env5$variable 0.14819
## permanova.model10Levels.env5$Level:permanova.model10Levels.env5$variable 0.06860
## Residuals 0.11691
## F value
## permanova.model10Levels.env5$Level 0.001
## permanova.model10Levels.env5$variable 1.268
## permanova.model10Levels.env5$Level:permanova.model10Levels.env5$variable 0.587
## Residuals
## Pr(>F)
## permanova.model10Levels.env5$Level 0.982
## permanova.model10Levels.env5$variable 0.273
## permanova.model10Levels.env5$Level:permanova.model10Levels.env5$variable 0.741
## Residuals
leveneTest(permanova.model10Levels.model$value~permanova.model10Levels.model$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 0.0018 1
## 273
leveneTest(permanova.model10Levels.env1$value~permanova.model10Levels.env1$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 12.249 3.331e-12 ***
## 273
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10Levels.env2$value~permanova.model10Levels.env2$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 36.543 < 2.2e-16 ***
## 273
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10Levels.env3$value~permanova.model10Levels.env3$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 25.85 < 2.2e-16 ***
## 273
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10Levels.env4$value~permanova.model10Levels.env4$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 22.639 < 2.2e-16 ***
## 273
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10Levels.env5$value~permanova.model10Levels.env5$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 7.4037 2.356e-07 ***
## 273
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Let’s say we want to know the effect of undersampling interacts with our normalization protocol to affect our ability to detect relationships between taxa and the environment. We can vary the sequencing depth:
# make sequencing depth ####
#method<-c("QSeq0.5", "QSeq1", "QSeq2", "QSeq3", "QSeq10")
model10.C1<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=100, V=50, method)
model10.C2<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=200, V=100, method)
model10.C3<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=250, method)
model10.C4<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=1000, V=500, method)
model10.C5<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=2000, V=1000, method)
LII output:
SummaryLII.model10.C1<-as.data.frame(Summarize.LII(model10.C1,method2))
SummaryLII.model10.C2<-as.data.frame(Summarize.LII(model10.C2, method2))
SummaryLII.model10.C3<-as.data.frame(Summarize.LII(model10.C3, method2))
SummaryLII.model10.C4<-as.data.frame(Summarize.LII(model10.C4, method2))
SummaryLII.model10.C5<-as.data.frame(Summarize.LII(model10.C5, method2))
# prepare data for merging datasets
SummaryLII.model10.C1$Level<-c(rep(100,10))
SummaryLII.model10.C1<-melt(SummaryLII.model10.C1, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C2$Level<-c(rep(200,10))
SummaryLII.model10.C2<-melt(SummaryLII.model10.C2, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C3$Level<-c(rep(500,10))
SummaryLII.model10.C3<-melt(SummaryLII.model10.C3, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C4$Level<-c(rep(1000,10))
SummaryLII.model10.C4<-melt(SummaryLII.model10.C4, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C5$Level<-c(rep(2000,10))
SummaryLII.model10.C5<-melt(SummaryLII.model10.C5, id.vars = "Level", measure.vars = method2)
# merge datasets
model10.SeqLevels<-do.call("rbind", list(SummaryLII.model10.C1,SummaryLII.model10.C2,SummaryLII.model10.C3,SummaryLII.model10.C4,SummaryLII.model10.C5))
# summarize for plotting
model10.SeqLevels.summary<-data_summary(model10.SeqLevels, varname="value", groupnames=c("Level", "variable"))
model10.SeqLevels.summary2<-data_summary2(model10.SeqLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(model10.SeqLevels.summary, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(30)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Sequencing Depth")+
ylab("LII Value (Mean +/- sd)")+
theme_classic()
ggplot(model10.SeqLevels.summary2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Sequencing Depth")+
ylab("LII Value (Median +/- min/max)")+
theme_classic()
These results are consistent with our previous experiment, where QSeq2-100 lose the least information; QSeq0.5 generally performs the worst, and un-normalized data only loses more information than QSeq0.5 and under certain conditions QSeq1. All methods perform best at highest sequencing depth.
Now let’s look at how well the environmental gradients predicts taxon abundance:
# sequencing depth env. lm ratio ####
SM.lmRatio.model10.C1<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1,method2))
SV.lmRatio.model10.C1<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1,method2))
SM.lmRatio.model10.C2<-as.data.frame(Summarize.lmRatiotab.Median(model10.C2,method2))
SV.lmRatio.model10.C2<-as.data.frame(Summarize.lmRatiotab.Var(model10.C2,method2))
SM.lmRatio.model10.C3<-as.data.frame(Summarize.lmRatiotab.Median(model10.C3,method2))
SV.lmRatio.model10.C3<-as.data.frame(Summarize.lmRatiotab.Var(model10.C3,method2))
SM.lmRatio.model10.C4<-as.data.frame(Summarize.lmRatiotab.Median(model10.C4,method2))
SV.lmRatio.model10.C4<-as.data.frame(Summarize.lmRatiotab.Var(model10.C4,method2))
SM.lmRatio.model10.C5<-as.data.frame(Summarize.lmRatiotab.Median(model10.C5,method2))
SV.lmRatio.model10.C5<-as.data.frame(Summarize.lmRatiotab.Var(model10.C5,method2))
# prepare data for merging datasets
SM.lmRatio.model10.C1$Level<-c(rep(100,10))
SV.lmRatio.model10.C1$Level<-c(rep(100,10))
SM.lmRatio.model10.C2$Level<-c(rep(200,10))
SV.lmRatio.model10.C2$Level<-c(rep(200,10))
SM.lmRatio.model10.C3$Level<-c(rep(500,10))
SV.lmRatio.model10.C3$Level<-c(rep(500,10))
SM.lmRatio.model10.C4$Level<-c(rep(1000,10))
SV.lmRatio.model10.C4$Level<-c(rep(1000,10))
SM.lmRatio.model10.C5$Level<-c(rep(2000,10))
SV.lmRatio.model10.C5$Level<-c(rep(2000,10))
SM.lmRatio.model10.C1<-melt(SM.lmRatio.model10.C1, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1<-melt(SV.lmRatio.model10.C1, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C2<-melt(SM.lmRatio.model10.C2, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C2<-melt(SV.lmRatio.model10.C2, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C3<-melt(SM.lmRatio.model10.C3, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C3<-melt(SV.lmRatio.model10.C3, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C4<-melt(SM.lmRatio.model10.C4, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C4<-melt(SV.lmRatio.model10.C4, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C5<-melt(SM.lmRatio.model10.C5, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C5<-melt(SV.lmRatio.model10.C5, id.vars = "Level", measure.vars = method2)
# merge datasets
SM.lmRatio.model10.CLevels<-do.call("rbind", list(SM.lmRatio.model10.C1,SM.lmRatio.model10.C2,SM.lmRatio.model10.C3,SM.lmRatio.model10.C4, SM.lmRatio.model10.C5))
SV.lmRatio.model10.CLevels<-do.call("rbind", list(SV.lmRatio.model10.C1,SV.lmRatio.model10.C2,SV.lmRatio.model10.C3,SV.lmRatio.model10.C4, SV.lmRatio.model10.C5))
# summarize for plotting
SM.lmRatio.model10C.p<-data_summary(SM.lmRatio.model10.CLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10C.p<-data_summary(SV.lmRatio.model10.CLevels, varname="value", groupnames=c("Level", "variable"))
# plot
SM.lmRatio.model10C.p2<-data_summary2(SM.lmRatio.model10.CLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10C.p2<-data_summary2(SV.lmRatio.model10.CLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatio.model10C.p, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(30)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Sampling Depth")+
ylab("Median lmRatio (Mean +/- sd)")+
theme_classic()
ggplot(SV.lmRatio.model10C.p, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(30)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Sampling Depth")+
ylab("Variance lmRatio (Mean +/- sd)")+
theme_classic()
ggplot(SM.lmRatio.model10C.p2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Sampling Depth")+
ylab("Median lmRatio (Median +/- min/max)")+
theme_classic()
ggplot(SV.lmRatio.model10C.p2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Sampling Depth")+
ylab("Variance lmRatio (Median +/- min/max)")+
theme_classic()
Typcially QSeq0.5 performs poorly, while other methods are essentially comparable. Often at low sequencing depth, un-normalized data has a performance that is somewhere between the QSeq1 and QSeq0.5 data. In some runs of the simulation it is a significant effect, in others it is not.
summary(aov(SM.lmRatio.model10.CLevels$value~SM.lmRatio.model10.CLevels$Level*SM.lmRatio.model10.CLevels$variable))
## Df
## SM.lmRatio.model10.CLevels$Level 1
## SM.lmRatio.model10.CLevels$variable 6
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable 6
## Residuals 336
## Sum Sq
## SM.lmRatio.model10.CLevels$Level 0.00827
## SM.lmRatio.model10.CLevels$variable 0.04372
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable 0.03204
## Residuals 0.19790
## Mean Sq
## SM.lmRatio.model10.CLevels$Level 0.008267
## SM.lmRatio.model10.CLevels$variable 0.007286
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable 0.005340
## Residuals 0.000589
## F value
## SM.lmRatio.model10.CLevels$Level 14.036
## SM.lmRatio.model10.CLevels$variable 12.371
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable 9.067
## Residuals
## Pr(>F)
## SM.lmRatio.model10.CLevels$Level 0.000211
## SM.lmRatio.model10.CLevels$variable 1.36e-12
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable 3.37e-09
## Residuals
##
## SM.lmRatio.model10.CLevels$Level ***
## SM.lmRatio.model10.CLevels$variable ***
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SM.lmRatio.model10.CLevels$value~SM.lmRatio.model10.CLevels$Level*SM.lmRatio.model10.CLevels$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatio.model10.CLevels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatio.model10.CLevels$Level, SM.lmRatio.model10.CLevels$variable
## Warning in TukeyHSD.aov(aov(SM.lmRatio.model10.CLevels$value ~
## SM.lmRatio.model10.CLevels$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SM.lmRatio.model10.CLevels$value ~ SM.lmRatio.model10.CLevels$Level * SM.lmRatio.model10.CLevels$variable)
##
## $`SM.lmRatio.model10.CLevels$variable`
## diff lwr upr p adj
## QSeq0.5-raw -3.277554e-02 -0.04717334 -0.01837774 0.0000000
## QSeq1-raw -4.357810e-03 -0.01875561 0.01003999 0.9727401
## QSeq2-raw -2.019430e-03 -0.01641723 0.01237837 0.9995974
## QSeq3-raw -2.913451e-04 -0.01468914 0.01410645 1.0000000
## QSeq10-raw -3.168551e-05 -0.01442949 0.01436611 1.0000000
## QSeq100-raw -3.637026e-05 -0.01443417 0.01436143 1.0000000
## QSeq1-QSeq0.5 2.841773e-02 0.01401993 0.04281553 0.0000002
## QSeq2-QSeq0.5 3.075611e-02 0.01635831 0.04515391 0.0000000
## QSeq3-QSeq0.5 3.248419e-02 0.01808639 0.04688199 0.0000000
## QSeq10-QSeq0.5 3.274385e-02 0.01834605 0.04714165 0.0000000
## QSeq100-QSeq0.5 3.273917e-02 0.01834137 0.04713697 0.0000000
## QSeq2-QSeq1 2.338381e-03 -0.01205942 0.01673618 0.9990658
## QSeq3-QSeq1 4.066465e-03 -0.01033133 0.01846426 0.9808036
## QSeq10-QSeq1 4.326125e-03 -0.01007167 0.01872392 0.9737193
## QSeq100-QSeq1 4.321440e-03 -0.01007636 0.01871924 0.9738619
## QSeq3-QSeq2 1.728084e-03 -0.01266972 0.01612588 0.9998371
## QSeq10-QSeq2 1.987744e-03 -0.01241006 0.01638554 0.9996326
## QSeq100-QSeq2 1.983059e-03 -0.01241474 0.01638086 0.9996376
## QSeq10-QSeq3 2.596596e-04 -0.01413814 0.01465746 1.0000000
## QSeq100-QSeq3 2.549749e-04 -0.01414282 0.01465277 1.0000000
## QSeq100-QSeq10 -4.684748e-06 -0.01440248 0.01439311 1.0000000
summary(aov(SV.lmRatio.model10.CLevels$value~SV.lmRatio.model10.CLevels$Level*SV.lmRatio.model10.CLevels$variable))
## Df Sum Sq
## SV.lmRatio.model10.CLevels$Level 1 0.2656
## SV.lmRatio.model10.CLevels$variable 6 0.3620
## SV.lmRatio.model10.CLevels$Level:SV.lmRatio.model10.CLevels$variable 6 0.0176
## Residuals 336 2.5287
## Mean Sq
## SV.lmRatio.model10.CLevels$Level 0.26562
## SV.lmRatio.model10.CLevels$variable 0.06033
## SV.lmRatio.model10.CLevels$Level:SV.lmRatio.model10.CLevels$variable 0.00294
## Residuals 0.00753
## F value
## SV.lmRatio.model10.CLevels$Level 35.295
## SV.lmRatio.model10.CLevels$variable 8.017
## SV.lmRatio.model10.CLevels$Level:SV.lmRatio.model10.CLevels$variable 0.390
## Residuals
## Pr(>F)
## SV.lmRatio.model10.CLevels$Level 7.08e-09
## SV.lmRatio.model10.CLevels$variable 4.24e-08
## SV.lmRatio.model10.CLevels$Level:SV.lmRatio.model10.CLevels$variable 0.885
## Residuals
##
## SV.lmRatio.model10.CLevels$Level ***
## SV.lmRatio.model10.CLevels$variable ***
## SV.lmRatio.model10.CLevels$Level:SV.lmRatio.model10.CLevels$variable
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SV.lmRatio.model10.CLevels$value~SV.lmRatio.model10.CLevels$Level*SV.lmRatio.model10.CLevels$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatio.model10.CLevels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatio.model10.CLevels$Level, SV.lmRatio.model10.CLevels$variable
## Warning in TukeyHSD.aov(aov(SV.lmRatio.model10.CLevels$value ~
## SV.lmRatio.model10.CLevels$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SV.lmRatio.model10.CLevels$value ~ SV.lmRatio.model10.CLevels$Level * SV.lmRatio.model10.CLevels$variable)
##
## $`SV.lmRatio.model10.CLevels$variable`
## diff lwr upr p adj
## QSeq0.5-raw 3.104695e-02 -0.02041918 0.082513070 0.5561473
## QSeq1-raw -2.924599e-02 -0.08071212 0.022220129 0.6261669
## QSeq2-raw -5.477231e-02 -0.10623844 -0.003306191 0.0286068
## QSeq3-raw -5.303787e-02 -0.10450399 -0.001571746 0.0385466
## QSeq10-raw -5.727050e-02 -0.10873662 -0.005804376 0.0182487
## QSeq100-raw -5.720414e-02 -0.10867026 -0.005738015 0.0184735
## QSeq1-QSeq0.5 -6.029294e-02 -0.11175906 -0.008826818 0.0102743
## QSeq2-QSeq0.5 -8.581926e-02 -0.13728538 -0.034353137 0.0000246
## QSeq3-QSeq0.5 -8.408482e-02 -0.13555094 -0.032618692 0.0000394
## QSeq10-QSeq0.5 -8.831745e-02 -0.13978357 -0.036851323 0.0000123
## QSeq100-QSeq0.5 -8.825109e-02 -0.13971721 -0.036784962 0.0000125
## QSeq2-QSeq1 -2.552632e-02 -0.07699244 0.025939804 0.7617524
## QSeq3-QSeq1 -2.379187e-02 -0.07525800 0.027674249 0.8167894
## QSeq10-QSeq1 -2.802451e-02 -0.07949063 0.023441619 0.6726082
## QSeq100-QSeq1 -2.795814e-02 -0.07942427 0.023507980 0.6750902
## QSeq3-QSeq2 1.734445e-03 -0.04973168 0.053200569 0.9999999
## QSeq10-QSeq2 -2.498185e-03 -0.05396431 0.048967938 0.9999992
## QSeq100-QSeq2 -2.431824e-03 -0.05389795 0.049034299 0.9999993
## QSeq10-QSeq3 -4.232630e-03 -0.05569875 0.047233493 0.9999824
## QSeq100-QSeq3 -4.166269e-03 -0.05563239 0.047299854 0.9999840
## QSeq100-QSeq10 6.636112e-05 -0.05139976 0.051532485 1.0000000
leveneTest(value~as.factor(Level)*variable, data=SV.lmRatio.model10.CLevels)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 34 1.0147 0.45
## 315
And same steps but for the categorical variables:
# lm ratio model sequencing depth ####
SM.lmRatioM.model10.C1<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1,method2))
SV.lmRatioM.model10.C1<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1,method2))
SM.lmRatioM.model10.C2<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C2,method2))
SV.lmRatioM.model10.C2<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C2,method2))
SM.lmRatioM.model10.C3<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C3,method2))
SV.lmRatioM.model10.C3<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C3,method2))
SM.lmRatioM.model10.C4<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C4,method2))
SV.lmRatioM.model10.C4<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C4,method2))
SM.lmRatioM.model10.C5<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C5,method2))
SV.lmRatioM.model10.C5<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C5,method2))
# prepare data for merging datasets
SM.lmRatioM.model10.C1$Level<-c(rep(100,10))
SV.lmRatioM.model10.C1$Level<-c(rep(100,10))
SM.lmRatioM.model10.C2$Level<-c(rep(200,10))
SV.lmRatioM.model10.C2$Level<-c(rep(200,10))
SM.lmRatioM.model10.C3$Level<-c(rep(500,10))
SV.lmRatioM.model10.C3$Level<-c(rep(500,10))
SM.lmRatioM.model10.C4$Level<-c(rep(1000,10))
SV.lmRatioM.model10.C4$Level<-c(rep(1000,10))
SM.lmRatioM.model10.C5$Level<-c(rep(2000,10))
SV.lmRatioM.model10.C5$Level<-c(rep(2000,10))
SM.lmRatioM.model10.C1<-melt(SM.lmRatioM.model10.C1, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C1<-melt(SV.lmRatioM.model10.C1, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.C2<-melt(SM.lmRatioM.model10.C2, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C2<-melt(SV.lmRatioM.model10.C2, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.C3<-melt(SM.lmRatioM.model10.C3, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C3<-melt(SV.lmRatioM.model10.C3, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.C4<-melt(SM.lmRatioM.model10.C4, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C4<-melt(SV.lmRatioM.model10.C4, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.C5<-melt(SM.lmRatioM.model10.C5, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C5<-melt(SV.lmRatioM.model10.C5, id.vars = "Level", measure.vars = method2)
# merge datasets
SM.lmRatioM.model10CLevels<-do.call("rbind", list(SM.lmRatioM.model10.C1,SM.lmRatioM.model10.C2,SM.lmRatioM.model10.C3,SM.lmRatioM.model10.C4, SM.lmRatioM.model10.C5))
SV.lmRatioM.model10CLevels<-do.call("rbind", list(SV.lmRatioM.model10.C1,SV.lmRatioM.model10.C2,SV.lmRatioM.model10.C3,SV.lmRatioM.model10.C4, SV.lmRatioM.model10.C5))
# summarize for plotting
SM.lmRatioM.model10C.p<-data_summary(SM.lmRatioM.model10CLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatioM.model10C.p<-data_summary(SV.lmRatioM.model10CLevels, varname="value", groupnames=c("Level", "variable"))
SM.lmRatioM.model10C.p2<-data_summary2(SM.lmRatioM.model10CLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatioM.model10C.p2<-data_summary2(SV.lmRatioM.model10CLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatioM.model10C.p, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(30)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Sequencing Depth")+
ylab("Median lmRatio.model (Mean +/- sd)")+
theme_classic()
ggplot(SV.lmRatioM.model10C.p, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(30)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Sequencing Depth")+
ylab("log Variance lmRatio.model (Mean +/- sd)")+
theme_classic()
ggplot(SM.lmRatioM.model10C.p2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Sequencing Depth")+
ylab("Median lmRatio.model (Median +/- min/max)")+
theme_classic()
ggplot(SV.lmRatioM.model10C.p2, aes(x=Level, y=log(value), group = variable, color=variable))+
geom_errorbar(aes(ymin=log(low), ymax=log(high)), width=.1, position=position_dodge(30)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Sequencing Depth")+
ylab("log Variance lmRatio.model (Median +/- min/max)")+
theme_classic()
It is typical for the categorical model to have greater agreement across the methods than the environmental gradients.
summary(aov(SM.lmRatioM.model10CLevels$value~SM.lmRatioM.model10CLevels$Level*SM.lmRatioM.model10CLevels$variable))
## Df
## SM.lmRatioM.model10CLevels$Level 1
## SM.lmRatioM.model10CLevels$variable 6
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable 6
## Residuals 336
## Sum Sq
## SM.lmRatioM.model10CLevels$Level 0.00521
## SM.lmRatioM.model10CLevels$variable 0.03459
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable 0.02608
## Residuals 0.21403
## Mean Sq
## SM.lmRatioM.model10CLevels$Level 0.005213
## SM.lmRatioM.model10CLevels$variable 0.005765
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable 0.004346
## Residuals 0.000637
## F value
## SM.lmRatioM.model10CLevels$Level 8.184
## SM.lmRatioM.model10CLevels$variable 9.050
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable 6.823
## Residuals
## Pr(>F)
## SM.lmRatioM.model10CLevels$Level 0.00449
## SM.lmRatioM.model10CLevels$variable 3.51e-09
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable 7.63e-07
## Residuals
##
## SM.lmRatioM.model10CLevels$Level **
## SM.lmRatioM.model10CLevels$variable ***
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SM.lmRatioM.model10CLevels$value~SM.lmRatioM.model10CLevels$Level*SM.lmRatioM.model10CLevels$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatioM.model10CLevels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatioM.model10CLevels$Level, SM.lmRatioM.model10CLevels$variable
## Warning in TukeyHSD.aov(aov(SM.lmRatioM.model10CLevels$value ~
## SM.lmRatioM.model10CLevels$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SM.lmRatioM.model10CLevels$value ~ SM.lmRatioM.model10CLevels$Level * SM.lmRatioM.model10CLevels$variable)
##
## $`SM.lmRatioM.model10CLevels$variable`
## diff lwr upr p adj
## QSeq0.5-raw -2.874458e-02 -0.04371771 -0.01377145 0.0000006
## QSeq1-raw -1.672331e-03 -0.01664546 0.01330080 0.9998931
## QSeq2-raw -5.878274e-04 -0.01556096 0.01438530 0.9999998
## QSeq3-raw -3.262371e-05 -0.01500575 0.01494051 1.0000000
## QSeq10-raw 2.109424e-15 -0.01497313 0.01497313 1.0000000
## QSeq100-raw 2.220446e-15 -0.01497313 0.01497313 1.0000000
## QSeq1-QSeq0.5 2.707225e-02 0.01209911 0.04204538 0.0000032
## QSeq2-QSeq0.5 2.815675e-02 0.01318362 0.04312988 0.0000010
## QSeq3-QSeq0.5 2.871195e-02 0.01373882 0.04368509 0.0000006
## QSeq10-QSeq0.5 2.874458e-02 0.01377145 0.04371771 0.0000006
## QSeq100-QSeq0.5 2.874458e-02 0.01377145 0.04371771 0.0000006
## QSeq2-QSeq1 1.084504e-03 -0.01388863 0.01605764 0.9999917
## QSeq3-QSeq1 1.639708e-03 -0.01333342 0.01661284 0.9999047
## QSeq10-QSeq1 1.672331e-03 -0.01330080 0.01664546 0.9998931
## QSeq100-QSeq1 1.672331e-03 -0.01330080 0.01664546 0.9998931
## QSeq3-QSeq2 5.552037e-04 -0.01441793 0.01552834 0.9999998
## QSeq10-QSeq2 5.878274e-04 -0.01438530 0.01556096 0.9999998
## QSeq100-QSeq2 5.878274e-04 -0.01438530 0.01556096 0.9999998
## QSeq10-QSeq3 3.262371e-05 -0.01494051 0.01500575 1.0000000
## QSeq100-QSeq3 3.262371e-05 -0.01494051 0.01500575 1.0000000
## QSeq100-QSeq10 1.110223e-16 -0.01497313 0.01497313 1.0000000
summary(aov(SV.lmRatioM.model10CLevels$value~SV.lmRatioM.model10CLevels$Level*SV.lmRatioM.model10CLevels$variable))
## Df Sum Sq
## SV.lmRatioM.model10CLevels$Level 1 0.1757
## SV.lmRatioM.model10CLevels$variable 6 0.3277
## SV.lmRatioM.model10CLevels$Level:SV.lmRatioM.model10CLevels$variable 6 0.0292
## Residuals 336 0.2823
## Mean Sq
## SV.lmRatioM.model10CLevels$Level 0.17568
## SV.lmRatioM.model10CLevels$variable 0.05462
## SV.lmRatioM.model10CLevels$Level:SV.lmRatioM.model10CLevels$variable 0.00487
## Residuals 0.00084
## F value
## SV.lmRatioM.model10CLevels$Level 209.129
## SV.lmRatioM.model10CLevels$variable 65.018
## SV.lmRatioM.model10CLevels$Level:SV.lmRatioM.model10CLevels$variable 5.802
## Residuals
## Pr(>F)
## SV.lmRatioM.model10CLevels$Level < 2e-16
## SV.lmRatioM.model10CLevels$variable < 2e-16
## SV.lmRatioM.model10CLevels$Level:SV.lmRatioM.model10CLevels$variable 9.1e-06
## Residuals
##
## SV.lmRatioM.model10CLevels$Level ***
## SV.lmRatioM.model10CLevels$variable ***
## SV.lmRatioM.model10CLevels$Level:SV.lmRatioM.model10CLevels$variable ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SV.lmRatioM.model10CLevels$value~SV.lmRatioM.model10CLevels$Level*SV.lmRatioM.model10CLevels$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatioM.model10CLevels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatioM.model10CLevels$Level, SV.lmRatioM.model10CLevels$variable
## Warning in TukeyHSD.aov(aov(SV.lmRatioM.model10CLevels$value ~
## SV.lmRatioM.model10CLevels$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SV.lmRatioM.model10CLevels$value ~ SV.lmRatioM.model10CLevels$Level * SV.lmRatioM.model10CLevels$variable)
##
## $`SV.lmRatioM.model10CLevels$variable`
## diff lwr upr p adj
## QSeq0.5-raw 0.0589309074 0.04173592 0.076125892 0.0000000
## QSeq1-raw 0.0057453442 -0.01144964 0.022940329 0.9557112
## QSeq2-raw -0.0210906251 -0.03828561 -0.003895640 0.0058233
## QSeq3-raw -0.0278245378 -0.04501952 -0.010629553 0.0000489
## QSeq10-raw -0.0329843348 -0.05017932 -0.015789350 0.0000006
## QSeq100-raw -0.0332472250 -0.05044221 -0.016052240 0.0000005
## QSeq1-QSeq0.5 -0.0531855633 -0.07038055 -0.035990578 0.0000000
## QSeq2-QSeq0.5 -0.0800215326 -0.09721652 -0.062826548 0.0000000
## QSeq3-QSeq0.5 -0.0867554452 -0.10395043 -0.069560460 0.0000000
## QSeq10-QSeq0.5 -0.0919152422 -0.10911023 -0.074720257 0.0000000
## QSeq100-QSeq0.5 -0.0921781324 -0.10937312 -0.074983148 0.0000000
## QSeq2-QSeq1 -0.0268359693 -0.04403095 -0.009640985 0.0001064
## QSeq3-QSeq1 -0.0335698820 -0.05076487 -0.016374897 0.0000003
## QSeq10-QSeq1 -0.0387296789 -0.05592466 -0.021534694 0.0000000
## QSeq100-QSeq1 -0.0389925691 -0.05618755 -0.021797584 0.0000000
## QSeq3-QSeq2 -0.0067339127 -0.02392890 0.010461072 0.9078826
## QSeq10-QSeq2 -0.0118937096 -0.02908869 0.005301275 0.3841698
## QSeq100-QSeq2 -0.0121565998 -0.02935158 0.005038385 0.3567277
## QSeq10-QSeq3 -0.0051597970 -0.02235478 0.012035188 0.9738926
## QSeq100-QSeq3 -0.0054226872 -0.02261767 0.011772298 0.9665702
## QSeq100-QSeq10 -0.0002628902 -0.01745787 0.016932095 1.0000000
Let’s look at the taxon relationships:
TaxRatio.model10.C1<-getTaxCor.Tab(model10.C1,method2)
TaxRatio.model10.C2<-getTaxCor.Tab(model10.C2,method2)
TaxRatio.model10.C3<-getTaxCor.Tab(model10.C3,method2)
TaxRatio.model10.C4<-getTaxCor.Tab(model10.C4,method2)
TaxRatio.model10.C5<-getTaxCor.Tab(model10.C5,method2)
V.TaxRatio.model10.C1<-melt(TaxRatio.model10.C1$V.tax)
M.TaxRatio.model10.C1<-melt(TaxRatio.model10.C1$Median.tax)
V.TaxRatio.model10.C2<-melt(TaxRatio.model10.C2$V.tax)
M.TaxRatio.model10.C2<-melt(TaxRatio.model10.C2$Median.tax)
V.TaxRatio.model10.C3<-melt(TaxRatio.model10.C3$V.tax)
M.TaxRatio.model10.C3<-melt(TaxRatio.model10.C3$Median.tax)
V.TaxRatio.model10.C4<-melt(TaxRatio.model10.C4$V.tax)
M.TaxRatio.model10.C4<-melt(TaxRatio.model10.C4$Median.tax)
V.TaxRatio.model10.C5<-melt(TaxRatio.model10.C5$V.tax)
M.TaxRatio.model10.C5<-melt(TaxRatio.model10.C5$Median.tax)
V.TaxRatio.model10.C1<-as.data.frame(V.TaxRatio.model10.C1)
M.TaxRatio.model10.C1<-as.data.frame(M.TaxRatio.model10.C1)
V.TaxRatio.model10.C2<-as.data.frame(V.TaxRatio.model10.C2)
M.TaxRatio.model10.C2<-as.data.frame(M.TaxRatio.model10.C2)
V.TaxRatio.model10.C3<-as.data.frame(V.TaxRatio.model10.C3)
M.TaxRatio.model10.C3<-as.data.frame(M.TaxRatio.model10.C3)
V.TaxRatio.model10.C4<-as.data.frame(V.TaxRatio.model10.C4)
M.TaxRatio.model10.C4<-as.data.frame(M.TaxRatio.model10.C4)
V.TaxRatio.model10.C5<-as.data.frame(V.TaxRatio.model10.C5)
M.TaxRatio.model10.C5<-as.data.frame(M.TaxRatio.model10.C5)
# prepare data for merging datasets
V.TaxRatio.model10.C1$Level<-c(rep(100,nrow(V.TaxRatio.model10.C1)))
V.TaxRatio.model10.C2$Level<-c(rep(200,nrow(V.TaxRatio.model10.C2)))
V.TaxRatio.model10.C3$Level<-c(rep(500,nrow(V.TaxRatio.model10.C3)))
V.TaxRatio.model10.C4$Level<-c(rep(1000,nrow(V.TaxRatio.model10.C4)))
V.TaxRatio.model10.C5$Level<-c(rep(2000,nrow(V.TaxRatio.model10.C5)))
M.TaxRatio.model10.C1$Level<-c(rep(100,nrow(M.TaxRatio.model10.C1)))
M.TaxRatio.model10.C2$Level<-c(rep(200,nrow(M.TaxRatio.model10.C2)))
M.TaxRatio.model10.C3$Level<-c(rep(500,nrow(M.TaxRatio.model10.C3)))
M.TaxRatio.model10.C4$Level<-c(rep(1000,nrow(M.TaxRatio.model10.C4)))
M.TaxRatio.model10.C5$Level<-c(rep(2000,nrow(M.TaxRatio.model10.C5)))
# merge datasets
V.TaxRatio.model10Levels<-do.call("rbind", list(V.TaxRatio.model10.C1,V.TaxRatio.model10.C2,V.TaxRatio.model10.C3,V.TaxRatio.model10.C4,V.TaxRatio.model10.C5))
M.TaxRatio.model10Levels<-do.call("rbind", list(M.TaxRatio.model10.C1,M.TaxRatio.model10.C2,M.TaxRatio.model10.C3,M.TaxRatio.model10.C4, M.TaxRatio.model10.C5))
# summarize for plotting
V.TaxRatio.model10.Seq.p<-data_summary(V.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.Seq.p<-data_summary(M.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
V.TaxRatio.model10.Seq.p2<-data_summary2(V.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.Seq.p2<-data_summary2(M.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
# plot
ggplot(V.TaxRatio.model10.Seq.p, aes(x=Level, y=value, group = Var2, color=Var2))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(100)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(100))+
geom_point(position=position_dodge(100))+
xlab("Sequencing Depth")+
ylab("Variance taxRatio (Mean +/- sd)")+
theme_classic()
ggplot(M.TaxRatio.model10.Seq.p, aes(x=Level, y=value, group = Var2, color=Var2))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(100)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(100))+
geom_point(position=position_dodge(100))+
xlab("Sequencing Depth")+
ylab("Median taxRatio (Mean +/- sd)")+
theme_classic()
ggplot(V.TaxRatio.model10.Seq.p2, aes(x=Level, y=log10(value), group = Var2, color=Var2))+
geom_errorbar(aes(ymin=log10(low), ymax=log10(high)), width=.1, position=position_dodge(100)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(100))+
geom_point(position=position_dodge(100))+
xlab("Sequencing Depth")+
ylab("log10 Variance taxRatio (Median +/- min/max)")+
theme_classic()
ggplot(M.TaxRatio.model10.Seq.p2, aes(x=Level, y=value, group = Var2, color=Var2))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(100)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(100))+
geom_point(position=position_dodge(100))+
xlab("Sequencing Depth")+
ylab("Median taxRatio (Median +/- min/max)")+
theme_classic()
Remember that variance should approach zero and mean should approach 1 in a perfect world. Greater deviations from these values represent less accurate retention of taxon-taxon relationships.
summary(aov(M.TaxRatio.model10Levels$value~M.TaxRatio.model10Levels$Level*M.TaxRatio.model10Levels$Var2))
## Df Sum Sq Mean Sq
## M.TaxRatio.model10Levels$Level 1 0.3 0.2539
## M.TaxRatio.model10Levels$Var2 6 5.2 0.8629
## M.TaxRatio.model10Levels$Level:M.TaxRatio.model10Levels$Var2 6 4.7 0.7752
## Residuals 336 319.5 0.9510
## F value Pr(>F)
## M.TaxRatio.model10Levels$Level 0.267 0.606
## M.TaxRatio.model10Levels$Var2 0.907 0.490
## M.TaxRatio.model10Levels$Level:M.TaxRatio.model10Levels$Var2 0.815 0.559
## Residuals
TukeyHSD(aov(M.TaxRatio.model10.Seq.p$value~M.TaxRatio.model10.Seq.p$Level*M.TaxRatio.model10.Seq.p$Var2))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## M.TaxRatio.model10.Seq.p$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## M.TaxRatio.model10.Seq.p$Level, M.TaxRatio.model10.Seq.p$Var2
## Warning in TukeyHSD.aov(aov(M.TaxRatio.model10.Seq.p$value ~
## M.TaxRatio.model10.Seq.p$Level * : 'which' specified some non-factors which will
## be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = M.TaxRatio.model10.Seq.p$value ~ M.TaxRatio.model10.Seq.p$Level * M.TaxRatio.model10.Seq.p$Var2)
##
## $`M.TaxRatio.model10.Seq.p$Var2`
## diff lwr upr p adj
## QSeq0.5-raw -0.4385739507 -1.1206615 0.2435136 0.3931872
## QSeq1-raw -0.2422962672 -0.9243838 0.4397913 0.9030558
## QSeq2-raw -0.1721212384 -0.8542088 0.5099663 0.9800260
## QSeq3-raw -0.1700517824 -0.8521394 0.5120358 0.9811991
## QSeq10-raw -0.1563827393 -0.8384703 0.5257048 0.9877236
## QSeq100-raw -0.1570590976 -0.8391467 0.5250285 0.9874477
## QSeq1-QSeq0.5 0.1962776835 -0.4858099 0.8783653 0.9621609
## QSeq2-QSeq0.5 0.2664527123 -0.4156349 0.9485403 0.8578009
## QSeq3-QSeq0.5 0.2685221683 -0.4135654 0.9506097 0.8534851
## QSeq10-QSeq0.5 0.2821912114 -0.3998964 0.9642788 0.8233586
## QSeq100-QSeq0.5 0.2815148531 -0.4005727 0.9636024 0.8249131
## QSeq2-QSeq1 0.0701750288 -0.6119125 0.7522626 0.9998579
## QSeq3-QSeq1 0.0722444848 -0.6098431 0.7543321 0.9998318
## QSeq10-QSeq1 0.0859135279 -0.5961741 0.7680011 0.9995427
## QSeq100-QSeq1 0.0852371696 -0.5968504 0.7673247 0.9995630
## QSeq3-QSeq2 0.0020694560 -0.6800181 0.6841570 1.0000000
## QSeq10-QSeq2 0.0157384991 -0.6663491 0.6978261 1.0000000
## QSeq100-QSeq2 0.0150621408 -0.6670254 0.6971497 1.0000000
## QSeq10-QSeq3 0.0136690431 -0.6684185 0.6957566 1.0000000
## QSeq100-QSeq3 0.0129926848 -0.6690949 0.6950803 1.0000000
## QSeq100-QSeq10 -0.0006763583 -0.6827639 0.6814112 1.0000000
summary(aov(V.TaxRatio.model10Levels$value~V.TaxRatio.model10Levels$Level*V.TaxRatio.model10Levels$Var2))
## Df Sum Sq
## V.TaxRatio.model10Levels$Level 1 3.313e+08
## V.TaxRatio.model10Levels$Var2 6 7.557e+09
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2 6 4.426e+09
## Residuals 336 5.719e+11
## Mean Sq F value
## V.TaxRatio.model10Levels$Level 3.313e+08 0.195
## V.TaxRatio.model10Levels$Var2 1.259e+09 0.740
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2 7.376e+08 0.433
## Residuals 1.702e+09
## Pr(>F)
## V.TaxRatio.model10Levels$Level 0.659
## V.TaxRatio.model10Levels$Var2 0.618
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2 0.856
## Residuals
TukeyHSD(aov(V.TaxRatio.model10Levels$value~V.TaxRatio.model10Levels$Level*V.TaxRatio.model10Levels$Var2))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10Levels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10Levels$Level, V.TaxRatio.model10Levels$Var2
## Warning in TukeyHSD.aov(aov(V.TaxRatio.model10Levels$value ~
## V.TaxRatio.model10Levels$Level * : 'which' specified some non-factors which will
## be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = V.TaxRatio.model10Levels$value ~ V.TaxRatio.model10Levels$Level * V.TaxRatio.model10Levels$Var2)
##
## $`V.TaxRatio.model10Levels$Var2`
## diff lwr upr p adj
## QSeq0.5-raw -14612.03415 -39088.42 9864.348 0.5687374
## QSeq1-raw -13534.61986 -38011.00 10941.762 0.6562404
## QSeq2-raw -12073.07256 -36549.45 12403.309 0.7664480
## QSeq3-raw -12834.68642 -37311.07 11641.695 0.7107766
## QSeq10-raw -12753.07522 -37229.46 11723.307 0.7169484
## QSeq100-raw -12861.78757 -37338.17 11614.594 0.7087173
## QSeq1-QSeq0.5 1077.41429 -23398.97 25553.796 0.9999996
## QSeq2-QSeq0.5 2538.96159 -21937.42 27015.343 0.9999307
## QSeq3-QSeq0.5 1777.34773 -22699.03 26253.730 0.9999916
## QSeq10-QSeq0.5 1858.95893 -22617.42 26335.341 0.9999890
## QSeq100-QSeq0.5 1750.24658 -22726.14 26226.628 0.9999923
## QSeq2-QSeq1 1461.54731 -23014.83 25937.929 0.9999974
## QSeq3-QSeq1 699.93344 -23776.45 25176.315 1.0000000
## QSeq10-QSeq1 781.54465 -23694.84 25257.926 0.9999999
## QSeq100-QSeq1 672.83229 -23803.55 25149.214 1.0000000
## QSeq3-QSeq2 -761.61387 -25238.00 23714.768 0.9999999
## QSeq10-QSeq2 -680.00266 -25156.38 23796.379 1.0000000
## QSeq100-QSeq2 -788.71502 -25265.10 23687.667 0.9999999
## QSeq10-QSeq3 81.61121 -24394.77 24557.993 1.0000000
## QSeq100-QSeq3 -27.10115 -24503.48 24449.281 1.0000000
## QSeq100-QSeq10 -108.71236 -24585.09 24367.669 1.0000000
model10C1.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1,method2, "CategoryRratio"))
model10C1.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1, method2, "F1Rratio"))
model10C1.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1, method2, "F2Rratio"))
model10C1.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1, method2, "F3Rratio"))
model10C1.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1, method2, "F4Rratio"))
model10C1.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1,method2, "F5Rratio"))
model10C2.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "CategoryRratio"))
model10C2.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "F1Rratio"))
model10C2.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "F2Rratio"))
model10C2.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "F3Rratio"))
model10C2.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "F4Rratio"))
model10C2.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "F5Rratio"))
model10C3.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "CategoryRratio"))
model10C3.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "F1Rratio"))
model10C3.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "F2Rratio"))
model10C3.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "F3Rratio"))
model10C3.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "F4Rratio"))
model10C3.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "F5Rratio"))
model10C4.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "CategoryRratio"))
model10C4.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "F1Rratio"))
model10C4.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "F2Rratio"))
model10C4.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "F3Rratio"))
model10C4.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "F4Rratio"))
model10C4.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "F5Rratio"))
model10C5.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "CategoryRratio"))
model10C5.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "F1Rratio"))
model10C5.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "F2Rratio"))
model10C5.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "F3Rratio"))
model10C5.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "F4Rratio"))
model10C5.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "F5Rratio"))
model10C1.Permanova.model$Level<-c(rep(100,10))
model10C1.Permanova.env1$Level<-c(rep(100,10))
model10C1.Permanova.env2$Level<-c(rep(100,10))
model10C1.Permanova.env3$Level<-c(rep(100,10))
model10C1.Permanova.env4$Level<-c(rep(100,10))
model10C1.Permanova.env5$Level<-c(rep(100,10))
model10C2.Permanova.model$Level<-c(rep(200,10))
model10C2.Permanova.env1$Level<-c(rep(200,10))
model10C2.Permanova.env2$Level<-c(rep(200,10))
model10C2.Permanova.env3$Level<-c(rep(200,10))
model10C2.Permanova.env4$Level<-c(rep(200,10))
model10C2.Permanova.env5$Level<-c(rep(200,10))
model10C3.Permanova.model$Level<-c(rep(500,10))
model10C3.Permanova.env1$Level<-c(rep(500,10))
model10C3.Permanova.env2$Level<-c(rep(500,10))
model10C3.Permanova.env3$Level<-c(rep(500,10))
model10C3.Permanova.env4$Level<-c(rep(500,10))
model10C3.Permanova.env5$Level<-c(rep(500,10))
model10C4.Permanova.model$Level<-c(rep(1000,10))
model10C4.Permanova.env1$Level<-c(rep(1000,10))
model10C4.Permanova.env2$Level<-c(rep(1000,10))
model10C4.Permanova.env3$Level<-c(rep(1000,10))
model10C4.Permanova.env4$Level<-c(rep(1000,10))
model10C4.Permanova.env5$Level<-c(rep(1000,10))
model10C5.Permanova.model$Level<-c(rep(2000,10))
model10C5.Permanova.env1$Level<-c(rep(2000,10))
model10C5.Permanova.env2$Level<-c(rep(2000,10))
model10C5.Permanova.env3$Level<-c(rep(2000,10))
model10C5.Permanova.env4$Level<-c(rep(2000,10))
model10C5.Permanova.env5$Level<-c(rep(2000,10))
permanova.model10CLevels.model<-do.call("rbind", list(model10C1.Permanova.model,model10C2.Permanova.model,model10C3.Permanova.model,model10C4.Permanova.model,model10C5.Permanova.model))
permanova.model10CLevels.env1<-do.call("rbind", list(model10C1.Permanova.env1,model10C2.Permanova.env1,model10C3.Permanova.env1,model10C4.Permanova.env1,model10C5.Permanova.env1))
permanova.model10CLevels.env2<-do.call("rbind", list(model10C1.Permanova.env2,model10C2.Permanova.env2,model10C3.Permanova.env2,model10C4.Permanova.env2,model10C5.Permanova.env2))
permanova.model10CLevels.env3<-do.call("rbind", list(model10C1.Permanova.env3,model10C2.Permanova.env3,model10C3.Permanova.env3,model10C4.Permanova.env3,model10C5.Permanova.env3))
permanova.model10CLevels.env4<-do.call("rbind", list(model10C1.Permanova.env4,model10C2.Permanova.env4,model10C3.Permanova.env4,model10C4.Permanova.env4,model10C5.Permanova.env4))
permanova.model10CLevels.env5<-do.call("rbind", list(model10C1.Permanova.env5,model10C2.Permanova.env5,model10C3.Permanova.env5,model10C4.Permanova.env5,model10C5.Permanova.env5))
permanova.model10CLevels.model<-melt(permanova.model10CLevels.model, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.env1<-melt(permanova.model10CLevels.env1, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.env2<-melt(permanova.model10CLevels.env2, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.env3<-melt(permanova.model10CLevels.env3, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.env4<-melt(permanova.model10CLevels.env4, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.env5<-melt(permanova.model10CLevels.env5, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.modelP<-data_summary2(permanova.model10CLevels.model, varname="value", groupnames=c("Level", "variable"))
permanova.model10CLevels.env1P<-data_summary2(permanova.model10CLevels.env1, varname="value", groupnames=c("Level", "variable"))
permanova.model10CLevels.env2P<-data_summary2(permanova.model10CLevels.env2, varname="value", groupnames=c("Level", "variable"))
permanova.model10CLevels.env3P<-data_summary2(permanova.model10CLevels.env3, varname="value", groupnames=c("Level", "variable"))
permanova.model10CLevels.env4P<-data_summary2(permanova.model10CLevels.env4, varname="value", groupnames=c("Level", "variable"))
permanova.model10CLevels.env5P<-data_summary2(permanova.model10CLevels.env5, varname="value", groupnames=c("Level", "variable"))
ggplot(permanova.model10CLevels.modelP, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Degree of Structure")+
ylab("Permanova modelRatio (Median +/- min/max)")+
theme_classic()
ggplot(permanova.model10CLevels.env1P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Degree of Structure")+
ylab("Permanova env1Ratio (Median +/- min/max)")+
theme_classic()
ggplot(permanova.model10CLevels.env2P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Degree of Structure")+
ylab("Permanova env2Ratio (Median +/- min/max)")+
theme_classic()
ggplot(permanova.model10CLevels.env3P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Degree of Structure")+
ylab("Permanova env3Ratio (Median +/- min/max)")+
theme_classic()
ggplot(permanova.model10CLevels.env4P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Degree of Structure")+
ylab("Permanova env4Ratio (Median +/- min/max)")+
theme_classic()
ggplot(permanova.model10CLevels.env5P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(30))+
geom_point(position=position_dodge(30))+
xlab("Degree of Structure")+
ylab("Permanova env5Ratio (Median +/- min/max)")+
theme_classic()
Again, results are similar to the sparcity example where the experimental design is equally strongly detected across normalization methods, but that un-normalized data significantly underperforms in capturing the relationship between community structure and the environmental gradients.
summary(aov(permanova.model10CLevels.model$value~permanova.model10CLevels.model$Level*permanova.model10CLevels.model$variable))
## Df
## permanova.model10CLevels.model$Level 1
## permanova.model10CLevels.model$variable 6
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CLevels.model$Level 0.08751
## permanova.model10CLevels.model$variable 0.00002
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable 0.00000
## Residuals 0.14051
## Mean Sq
## permanova.model10CLevels.model$Level 0.08751
## permanova.model10CLevels.model$variable 0.00000
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable 0.00000
## Residuals 0.00042
## F value
## permanova.model10CLevels.model$Level 209.260
## permanova.model10CLevels.model$variable 0.008
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable 0.001
## Residuals
## Pr(>F)
## permanova.model10CLevels.model$Level <2e-16
## permanova.model10CLevels.model$variable 1
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable 1
## Residuals
##
## permanova.model10CLevels.model$Level ***
## permanova.model10CLevels.model$variable
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CLevels.model$value~permanova.model10CLevels.model$Level*permanova.model10CLevels.model$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.model$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.model$Level, permanova.model10CLevels.model$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.model$value ~
## permanova.model10CLevels.model$Level * : 'which' specified some non-factors
## which will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CLevels.model$value ~ permanova.model10CLevels.model$Level * permanova.model10CLevels.model$variable)
##
## $`permanova.model10CLevels.model$variable`
## diff lwr upr p adj
## QSeq0.5-raw -7.208348e-04 -0.01285265 0.01141098 0.9999974
## QSeq1-raw -7.543226e-06 -0.01213935 0.01212427 1.0000000
## QSeq2-raw -1.117542e-04 -0.01224356 0.01202006 1.0000000
## QSeq3-raw -8.359712e-05 -0.01221541 0.01204821 1.0000000
## QSeq10-raw -1.663831e-05 -0.01214845 0.01211517 1.0000000
## QSeq100-raw -2.220446e-16 -0.01213181 0.01213181 1.0000000
## QSeq1-QSeq0.5 7.132915e-04 -0.01141852 0.01284510 0.9999976
## QSeq2-QSeq0.5 6.090806e-04 -0.01152273 0.01274089 0.9999991
## QSeq3-QSeq0.5 6.372376e-04 -0.01149457 0.01276905 0.9999988
## QSeq10-QSeq0.5 7.041965e-04 -0.01142761 0.01283601 0.9999978
## QSeq100-QSeq0.5 7.208348e-04 -0.01141098 0.01285265 0.9999974
## QSeq2-QSeq1 -1.042110e-04 -0.01223602 0.01202760 1.0000000
## QSeq3-QSeq1 -7.605389e-05 -0.01220786 0.01205576 1.0000000
## QSeq10-QSeq1 -9.095080e-06 -0.01214091 0.01212272 1.0000000
## QSeq100-QSeq1 7.543226e-06 -0.01212427 0.01213935 1.0000000
## QSeq3-QSeq2 2.815707e-05 -0.01210365 0.01215997 1.0000000
## QSeq10-QSeq2 9.511588e-05 -0.01203669 0.01222693 1.0000000
## QSeq100-QSeq2 1.117542e-04 -0.01202006 0.01224356 1.0000000
## QSeq10-QSeq3 6.695881e-05 -0.01206485 0.01219877 1.0000000
## QSeq100-QSeq3 8.359712e-05 -0.01204821 0.01221541 1.0000000
## QSeq100-QSeq10 1.663831e-05 -0.01211517 0.01214845 1.0000000
summary(aov(permanova.model10CLevels.env1$value~permanova.model10CLevels.env1$Level*permanova.model10CLevels.env1$variable))
## Df
## permanova.model10CLevels.env1$Level 1
## permanova.model10CLevels.env1$variable 6
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CLevels.env1$Level 0.0425
## permanova.model10CLevels.env1$variable 0.4600
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable 0.0864
## Residuals 1.1354
## Mean Sq
## permanova.model10CLevels.env1$Level 0.04249
## permanova.model10CLevels.env1$variable 0.07667
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable 0.01439
## Residuals 0.00338
## F value
## permanova.model10CLevels.env1$Level 12.574
## permanova.model10CLevels.env1$variable 22.689
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable 4.259
## Residuals
## Pr(>F)
## permanova.model10CLevels.env1$Level 0.000447
## permanova.model10CLevels.env1$variable < 2e-16
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable 0.000376
## Residuals
##
## permanova.model10CLevels.env1$Level ***
## permanova.model10CLevels.env1$variable ***
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CLevels.env1$value~permanova.model10CLevels.env1$Level*permanova.model10CLevels.env1$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env1$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env1$Level, permanova.model10CLevels.env1$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.env1$value ~
## permanova.model10CLevels.env1$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CLevels.env1$value ~ permanova.model10CLevels.env1$Level * permanova.model10CLevels.env1$variable)
##
## $`permanova.model10CLevels.env1$variable`
## diff lwr upr p adj
## QSeq0.5-raw 1.030146e-01 0.06852811 0.13750101 0
## QSeq1-raw 1.032224e-01 0.06873592 0.13770882 0
## QSeq2-raw 1.037682e-01 0.06928172 0.13825462 0
## QSeq3-raw 1.038404e-01 0.06935391 0.13832681 0
## QSeq10-raw 1.038662e-01 0.06937978 0.13835268 0
## QSeq100-raw 1.038909e-01 0.06940448 0.13837739 0
## QSeq1-QSeq0.5 2.078109e-04 -0.03427864 0.03469426 1
## QSeq2-QSeq0.5 7.536109e-04 -0.03373284 0.03524006 1
## QSeq3-QSeq0.5 8.257986e-04 -0.03366065 0.03531225 1
## QSeq10-QSeq0.5 8.516714e-04 -0.03363478 0.03533812 1
## QSeq100-QSeq0.5 8.763743e-04 -0.03361008 0.03536283 1
## QSeq2-QSeq1 5.458000e-04 -0.03394065 0.03503225 1
## QSeq3-QSeq1 6.179877e-04 -0.03386847 0.03510444 1
## QSeq10-QSeq1 6.438605e-04 -0.03384259 0.03513031 1
## QSeq100-QSeq1 6.685634e-04 -0.03381789 0.03515502 1
## QSeq3-QSeq2 7.218769e-05 -0.03441427 0.03455864 1
## QSeq10-QSeq2 9.806049e-05 -0.03438839 0.03458451 1
## QSeq100-QSeq2 1.227634e-04 -0.03436369 0.03460922 1
## QSeq10-QSeq3 2.587280e-05 -0.03446058 0.03451233 1
## QSeq100-QSeq3 5.057568e-05 -0.03443588 0.03453703 1
## QSeq100-QSeq10 2.470288e-05 -0.03446175 0.03451116 1
summary(aov(permanova.model10CLevels.env2$value~permanova.model10CLevels.env2$Level*permanova.model10CLevels.env2$variable))
## Df
## permanova.model10CLevels.env2$Level 1
## permanova.model10CLevels.env2$variable 6
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CLevels.env2$Level 0.1220
## permanova.model10CLevels.env2$variable 2.2082
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable 0.0007
## Residuals 1.8823
## Mean Sq
## permanova.model10CLevels.env2$Level 0.1220
## permanova.model10CLevels.env2$variable 0.3680
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable 0.0001
## Residuals 0.0056
## F value
## permanova.model10CLevels.env2$Level 21.777
## permanova.model10CLevels.env2$variable 65.698
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable 0.022
## Residuals
## Pr(>F)
## permanova.model10CLevels.env2$Level 4.43e-06
## permanova.model10CLevels.env2$variable < 2e-16
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable 1
## Residuals
##
## permanova.model10CLevels.env2$Level ***
## permanova.model10CLevels.env2$variable ***
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CLevels.env2$value~permanova.model10CLevels.env2$Level*permanova.model10CLevels.env2$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env2$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env2$Level, permanova.model10CLevels.env2$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.env2$value ~
## permanova.model10CLevels.env2$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CLevels.env2$value ~ permanova.model10CLevels.env2$Level * permanova.model10CLevels.env2$variable)
##
## $`permanova.model10CLevels.env2$variable`
## diff lwr upr p adj
## QSeq0.5-raw 2.266910e-01 0.18228744 0.27109456 0
## QSeq1-raw 2.265421e-01 0.18213854 0.27094566 0
## QSeq2-raw 2.271302e-01 0.18272661 0.27153372 0
## QSeq3-raw 2.272645e-01 0.18286094 0.27166806 0
## QSeq10-raw 2.271532e-01 0.18274965 0.27155677 0
## QSeq100-raw 2.271662e-01 0.18276268 0.27156980 0
## QSeq1-QSeq0.5 -1.489028e-04 -0.04455246 0.04425465 1
## QSeq2-QSeq0.5 4.391645e-04 -0.04396439 0.04484272 1
## QSeq3-QSeq0.5 5.734981e-04 -0.04383006 0.04497706 1
## QSeq10-QSeq0.5 4.622074e-04 -0.04394135 0.04486577 1
## QSeq100-QSeq0.5 4.752397e-04 -0.04392832 0.04487880 1
## QSeq2-QSeq1 5.880674e-04 -0.04381549 0.04499163 1
## QSeq3-QSeq1 7.224010e-04 -0.04368116 0.04512596 1
## QSeq10-QSeq1 6.111103e-04 -0.04379245 0.04501467 1
## QSeq100-QSeq1 6.241426e-04 -0.04377942 0.04502770 1
## QSeq3-QSeq2 1.343336e-04 -0.04426922 0.04453789 1
## QSeq10-QSeq2 2.304294e-05 -0.04438051 0.04442660 1
## QSeq100-QSeq2 3.607523e-05 -0.04436748 0.04443963 1
## QSeq10-QSeq3 -1.112907e-04 -0.04451485 0.04429227 1
## QSeq100-QSeq3 -9.825840e-05 -0.04450182 0.04430530 1
## QSeq100-QSeq10 1.303230e-05 -0.04439053 0.04441659 1
summary(aov(permanova.model10CLevels.env3$value~permanova.model10CLevels.env3$Level*permanova.model10CLevels.env3$variable))
## Df
## permanova.model10CLevels.env3$Level 1
## permanova.model10CLevels.env3$variable 6
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CLevels.env3$Level 0.0771
## permanova.model10CLevels.env3$variable 1.0067
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable 0.0694
## Residuals 1.1620
## Mean Sq
## permanova.model10CLevels.env3$Level 0.07705
## permanova.model10CLevels.env3$variable 0.16778
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable 0.01156
## Residuals 0.00346
## F value
## permanova.model10CLevels.env3$Level 22.281
## permanova.model10CLevels.env3$variable 48.516
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable 3.343
## Residuals
## Pr(>F)
## permanova.model10CLevels.env3$Level 3.46e-06
## permanova.model10CLevels.env3$variable < 2e-16
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable 0.00327
## Residuals
##
## permanova.model10CLevels.env3$Level ***
## permanova.model10CLevels.env3$variable ***
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable **
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CLevels.env3$value~permanova.model10CLevels.env3$Level*permanova.model10CLevels.env3$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env3$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env3$Level, permanova.model10CLevels.env3$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.env3$value ~
## permanova.model10CLevels.env3$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CLevels.env3$value ~ permanova.model10CLevels.env3$Level * permanova.model10CLevels.env3$variable)
##
## $`permanova.model10CLevels.env3$variable`
## diff lwr upr p adj
## QSeq0.5-raw 1.534585e-01 0.11857061 0.18834645 0
## QSeq1-raw 1.534241e-01 0.11853622 0.18831206 0
## QSeq2-raw 1.528069e-01 0.11791902 0.18769486 0
## QSeq3-raw 1.530648e-01 0.11817684 0.18795267 0
## QSeq10-raw 1.533822e-01 0.11849430 0.18827014 0
## QSeq100-raw 1.534322e-01 0.11854428 0.18832012 0
## QSeq1-QSeq0.5 -3.439159e-05 -0.03492231 0.03485353 1
## QSeq2-QSeq0.5 -6.515900e-04 -0.03553951 0.03423633 1
## QSeq3-QSeq0.5 -3.937750e-04 -0.03528169 0.03449414 1
## QSeq10-QSeq0.5 -7.631251e-05 -0.03496423 0.03481161 1
## QSeq100-QSeq0.5 -2.632669e-05 -0.03491425 0.03486159 1
## QSeq2-QSeq1 -6.171984e-04 -0.03550512 0.03427072 1
## QSeq3-QSeq1 -3.593834e-04 -0.03524730 0.03452854 1
## QSeq10-QSeq1 -4.192093e-05 -0.03492984 0.03484600 1
## QSeq100-QSeq1 8.064893e-06 -0.03487985 0.03489598 1
## QSeq3-QSeq2 2.578150e-04 -0.03463010 0.03514573 1
## QSeq10-QSeq2 5.752775e-04 -0.03431264 0.03546320 1
## QSeq100-QSeq2 6.252633e-04 -0.03426266 0.03551318 1
## QSeq10-QSeq3 3.174625e-04 -0.03457046 0.03520538 1
## QSeq100-QSeq3 3.674483e-04 -0.03452047 0.03525537 1
## QSeq100-QSeq10 4.998582e-05 -0.03483793 0.03493790 1
summary(aov(permanova.model10CLevels.env4$value~permanova.model10CLevels.env4$Level*permanova.model10CLevels.env4$variable))
## Df
## permanova.model10CLevels.env4$Level 1
## permanova.model10CLevels.env4$variable 6
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CLevels.env4$Level 0.080
## permanova.model10CLevels.env4$variable 0.358
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable 0.036
## Residuals 5.974
## Mean Sq
## permanova.model10CLevels.env4$Level 0.08003
## permanova.model10CLevels.env4$variable 0.05962
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable 0.00602
## Residuals 0.01778
## F value
## permanova.model10CLevels.env4$Level 4.501
## permanova.model10CLevels.env4$variable 3.354
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable 0.339
## Residuals
## Pr(>F)
## permanova.model10CLevels.env4$Level 0.03460
## permanova.model10CLevels.env4$variable 0.00319
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable 0.91619
## Residuals
##
## permanova.model10CLevels.env4$Level *
## permanova.model10CLevels.env4$variable **
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CLevels.env4$value~permanova.model10CLevels.env4$Level*permanova.model10CLevels.env4$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env4$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env4$Level, permanova.model10CLevels.env4$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.env4$value ~
## permanova.model10CLevels.env4$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CLevels.env4$value ~ permanova.model10CLevels.env4$Level * permanova.model10CLevels.env4$variable)
##
## $`permanova.model10CLevels.env4$variable`
## diff lwr upr p adj
## QSeq0.5-raw 0.0920573542 0.01295399 0.17116072 0.0111039
## QSeq1-raw 0.0928939089 0.01379054 0.17199728 0.0099857
## QSeq2-raw 0.0895486165 0.01044525 0.16865198 0.0151694
## QSeq3-raw 0.0909219827 0.01181862 0.17002535 0.0128030
## QSeq10-raw 0.0913350074 0.01223164 0.17043838 0.0121595
## QSeq100-raw 0.0911812149 0.01207785 0.17028458 0.0123956
## QSeq1-QSeq0.5 0.0008365547 -0.07826681 0.07993992 1.0000000
## QSeq2-QSeq0.5 -0.0025087377 -0.08161211 0.07659463 0.9999999
## QSeq3-QSeq0.5 -0.0011353716 -0.08023874 0.07796800 1.0000000
## QSeq10-QSeq0.5 -0.0007223469 -0.07982571 0.07838102 1.0000000
## QSeq100-QSeq0.5 -0.0008761393 -0.07997951 0.07822723 1.0000000
## QSeq2-QSeq1 -0.0033452924 -0.08244866 0.07575808 0.9999997
## QSeq3-QSeq1 -0.0019719262 -0.08107529 0.07713144 1.0000000
## QSeq10-QSeq1 -0.0015589015 -0.08066227 0.07754447 1.0000000
## QSeq100-QSeq1 -0.0017126940 -0.08081606 0.07739067 1.0000000
## QSeq3-QSeq2 0.0013733661 -0.07773000 0.08047673 1.0000000
## QSeq10-QSeq2 0.0017863908 -0.07731698 0.08088976 1.0000000
## QSeq100-QSeq2 0.0016325984 -0.07747077 0.08073597 1.0000000
## QSeq10-QSeq3 0.0004130247 -0.07869034 0.07951639 1.0000000
## QSeq100-QSeq3 0.0002592323 -0.07884414 0.07936260 1.0000000
## QSeq100-QSeq10 -0.0001537924 -0.07925716 0.07894958 1.0000000
summary(aov(permanova.model10CLevels.env5$value~permanova.model10CLevels.env5$Level*permanova.model10CLevels.env5$variable))
## Df
## permanova.model10CLevels.env5$Level 1
## permanova.model10CLevels.env5$variable 6
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CLevels.env5$Level 0.042
## permanova.model10CLevels.env5$variable 2.131
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable 0.027
## Residuals 4.465
## Mean Sq
## permanova.model10CLevels.env5$Level 0.0424
## permanova.model10CLevels.env5$variable 0.3551
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable 0.0045
## Residuals 0.0133
## F value
## permanova.model10CLevels.env5$Level 3.190
## permanova.model10CLevels.env5$variable 26.727
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable 0.342
## Residuals
## Pr(>F)
## permanova.model10CLevels.env5$Level 0.075
## permanova.model10CLevels.env5$variable <2e-16
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable 0.915
## Residuals
##
## permanova.model10CLevels.env5$Level .
## permanova.model10CLevels.env5$variable ***
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CLevels.env5$value~permanova.model10CLevels.env5$Level*permanova.model10CLevels.env5$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env5$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env5$Level, permanova.model10CLevels.env5$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.env5$value ~
## permanova.model10CLevels.env5$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CLevels.env5$value ~ permanova.model10CLevels.env5$Level * permanova.model10CLevels.env5$variable)
##
## $`permanova.model10CLevels.env5$variable`
## diff lwr upr p adj
## QSeq0.5-raw 2.224973e-01 0.15411109 0.29088359 0
## QSeq1-raw 2.231785e-01 0.15479222 0.29156472 0
## QSeq2-raw 2.238929e-01 0.15550666 0.29227916 0
## QSeq3-raw 2.225283e-01 0.15414208 0.29091458 0
## QSeq10-raw 2.228817e-01 0.15449548 0.29126798 0
## QSeq100-raw 2.228581e-01 0.15447184 0.29124434 0
## QSeq1-QSeq0.5 6.811330e-04 -0.06770512 0.06906738 1
## QSeq2-QSeq0.5 1.395568e-03 -0.06699068 0.06978182 1
## QSeq3-QSeq0.5 3.098682e-05 -0.06835526 0.06841724 1
## QSeq10-QSeq0.5 3.843868e-04 -0.06800186 0.06877064 1
## QSeq100-QSeq0.5 3.607481e-04 -0.06802550 0.06874700 1
## QSeq2-QSeq1 7.144352e-04 -0.06767181 0.06910068 1
## QSeq3-QSeq1 -6.501462e-04 -0.06903640 0.06773610 1
## QSeq10-QSeq1 -2.967461e-04 -0.06868300 0.06808950 1
## QSeq100-QSeq1 -3.203849e-04 -0.06870663 0.06806586 1
## QSeq3-QSeq2 -1.364581e-03 -0.06975083 0.06702167 1
## QSeq10-QSeq2 -1.011181e-03 -0.06939743 0.06737507 1
## QSeq100-QSeq2 -1.034820e-03 -0.06942107 0.06735143 1
## QSeq10-QSeq3 3.534000e-04 -0.06803285 0.06873965 1
## QSeq100-QSeq3 3.297613e-04 -0.06805649 0.06871601 1
## QSeq100-QSeq10 -2.363877e-05 -0.06840989 0.06836261 1
leveneTest(permanova.model10CLevels.model$value~permanova.model10CLevels.model$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 0.001 1
## 343
leveneTest(permanova.model10CLevels.env1$value~permanova.model10CLevels.env1$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 17.336 < 2.2e-16 ***
## 343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10CLevels.env2$value~permanova.model10CLevels.env2$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 28.579 < 2.2e-16 ***
## 343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10CLevels.env3$value~permanova.model10CLevels.env3$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 18.108 < 2.2e-16 ***
## 343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10CLevels.env4$value~permanova.model10CLevels.env4$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 19.103 < 2.2e-16 ***
## 343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10CLevels.env5$value~permanova.model10CLevels.env5$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 33.051 < 2.2e-16 ***
## 343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
By now you shuld be able to interpret the results; so I won’t explain everything (they are very consistent across experiments)
# sequencing variance ####
model10.C1V1<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=50, method)
model10.C1V2<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=100, method)
model10.C1V3<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=250, method)
model10.C1V4<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=500, method)
model10.C1V5<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=1000, method)
LII output:
# sequencing variants LII ####
SummaryLII.model10.C1V1<-as.data.frame(Summarize.LII(model10.C1V1, method2)) # actually C3 ...
SummaryLII.model10.C1V2<-as.data.frame(Summarize.LII(model10.C1V2, method2))
SummaryLII.model10.C1V3<-as.data.frame(Summarize.LII(model10.C1V3, method2))
SummaryLII.model10.C1V4<-as.data.frame(Summarize.LII(model10.C1V4, method2))
SummaryLII.model10.C1V5<-as.data.frame(Summarize.LII(model10.C1V5, method2))
# prepare data for merging datasets
SummaryLII.model10.C1V1$Level<-c(rep(0.1,10))
SummaryLII.model10.C1V1<-melt(SummaryLII.model10.C1V1, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C1V2$Level<-c(rep(0.2,10))
SummaryLII.model10.C1V2<-melt(SummaryLII.model10.C1V2, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C1V3$Level<-c(rep(0.5,10))
SummaryLII.model10.C1V3<-melt(SummaryLII.model10.C1V3, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C1V4$Level<-c(rep(1,10))
SummaryLII.model10.C1V4<-melt(SummaryLII.model10.C1V4, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C1V5$Level<-c(rep(2,10))
SummaryLII.model10.C1V5<-melt(SummaryLII.model10.C1V5, id.vars = "Level", measure.vars = method2)
# merge datasets
model10.SeqVarLevels<-do.call("rbind", list(SummaryLII.model10.C1V1,SummaryLII.model10.C1V2,SummaryLII.model10.C1V3,SummaryLII.model10.C1V4,SummaryLII.model10.C1V5))
# summarize for plotting
model10.SeqVarLevels.summary<-data_summary(model10.SeqVarLevels, varname="value", groupnames=c("Level", "variable"))
model10.SeqVarLevels.summary2<-data_summary2(model10.SeqVarLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(model10.SeqVarLevels.summary, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.1)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.1))+
geom_point(position=position_dodge(.1))+
xlab("Sequencing Variance")+
ylab("LII Value (Mean +/- sd)")+
theme_classic()
ggplot(model10.SeqVarLevels.summary2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.1)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(.1))+
geom_point(position=position_dodge(.1))+
xlab("Sequencing Variance")+
ylab("LII Value (Median +/- min/max)")+
theme_classic()
summary(aov(SummaryLII.model10.C1V1$value~SummaryLII.model10.C1V1$Level*SummaryLII.model10.C1V1$variable))
## Df Sum Sq Mean Sq F value Pr(>F)
## SummaryLII.model10.C1V1$variable 6 0.09284 0.015473 12.7 2.44e-09 ***
## Residuals 63 0.07673 0.001218
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SummaryLII.model10.C1V1$value~SummaryLII.model10.C1V1$Level*SummaryLII.model10.C1V1$variable))
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SummaryLII.model10.C1V1$value ~ SummaryLII.model10.C1V1$Level * SummaryLII.model10.C1V1$variable)
##
## $`SummaryLII.model10.C1V1$variable`
## diff lwr upr p adj
## QSeq0.5-raw 0.0521144723 0.004579925 0.099649020 0.0226951
## QSeq1-raw -0.0157004439 -0.063234991 0.031834103 0.9508030
## QSeq2-raw -0.0455986466 -0.093133194 0.001935901 0.0683197
## QSeq3-raw -0.0489662830 -0.096500830 -0.001431736 0.0393541
## QSeq10-raw -0.0535323011 -0.101066848 -0.005997754 0.0175333
## QSeq100-raw -0.0537387272 -0.101273275 -0.006204180 0.0168783
## QSeq1-QSeq0.5 -0.0678149162 -0.115349464 -0.020280369 0.0009735
## QSeq2-QSeq0.5 -0.0977131189 -0.145247666 -0.050178571 0.0000008
## QSeq3-QSeq0.5 -0.1010807553 -0.148615303 -0.053546208 0.0000003
## QSeq10-QSeq0.5 -0.1056467734 -0.153181321 -0.058112226 0.0000001
## QSeq100-QSeq0.5 -0.1058531995 -0.153387747 -0.058318652 0.0000001
## QSeq2-QSeq1 -0.0298982027 -0.077432750 0.017636345 0.4779547
## QSeq3-QSeq1 -0.0332658390 -0.080800386 0.014268708 0.3475771
## QSeq10-QSeq1 -0.0378318572 -0.085366405 0.009702690 0.2060281
## QSeq100-QSeq1 -0.0380382833 -0.085572831 0.009496264 0.2007434
## QSeq3-QSeq2 -0.0033676364 -0.050902184 0.044166911 0.9999909
## QSeq10-QSeq2 -0.0079336545 -0.055468202 0.039600893 0.9986504
## QSeq100-QSeq2 -0.0081400806 -0.055674628 0.039394467 0.9984402
## QSeq10-QSeq3 -0.0045660181 -0.052100566 0.042968529 0.9999447
## QSeq100-QSeq3 -0.0047724442 -0.052306992 0.042762103 0.9999283
## QSeq100-QSeq10 -0.0002064261 -0.047740974 0.047328121 1.0000000
linear model outputs:
# sequencing variants lm ####
SM.lmRatio.model10.C1V1<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1V1,method2))
SV.lmRatio.model10.C1V1<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1V1,method2))
SM.lmRatio.model10.C1V2<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1V2,method2))
SV.lmRatio.model10.C1V2<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1V2,method2))
SM.lmRatio.model10.C1V3<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1V3,method2))
SV.lmRatio.model10.C1V3<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1V3,method2))
SM.lmRatio.model10.C1V4<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1V4,method2))
SV.lmRatio.model10.C1V4<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1V4,method2))
SM.lmRatio.model10.C1V5<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1V5,method2))
SV.lmRatio.model10.C1V5<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1V5,method2))
# prepare data for merging datasets
SM.lmRatio.model10.C1V1$Level<-c(rep(0.1,10))
SV.lmRatio.model10.C1V1$Level<-c(rep(0.1,10))
SM.lmRatio.model10.C1V2$Level<-c(rep(0.2,10))
SV.lmRatio.model10.C1V2$Level<-c(rep(0.2,10))
SM.lmRatio.model10.C1V3$Level<-c(rep(0.5,10))
SV.lmRatio.model10.C1V3$Level<-c(rep(0.5,10))
SM.lmRatio.model10.C1V4$Level<-c(rep(1,10))
SV.lmRatio.model10.C1V4$Level<-c(rep(1,10))
SM.lmRatio.model10.C1V5$Level<-c(rep(2,10))
SV.lmRatio.model10.C1V5$Level<-c(rep(2,10))
SM.lmRatio.model10.C1V1<-melt(SM.lmRatio.model10.C1V1, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1V1<-melt(SV.lmRatio.model10.C1V1, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C1V2<-melt(SM.lmRatio.model10.C1V2, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1V2<-melt(SV.lmRatio.model10.C1V2, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C1V3<-melt(SM.lmRatio.model10.C1V3, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1V3<-melt(SV.lmRatio.model10.C1V3, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C1V4<-melt(SM.lmRatio.model10.C1V4, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1V4<-melt(SV.lmRatio.model10.C1V4, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C1V5<-melt(SM.lmRatio.model10.C1V5, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1V5<-melt(SV.lmRatio.model10.C1V5, id.vars = "Level", measure.vars = method2)
# merge datasets
SM.lmRatio.model10.CVLevels<-do.call("rbind", list(SM.lmRatio.model10.C1V1,SM.lmRatio.model10.C1V2,SM.lmRatio.model10.C1V3,SM.lmRatio.model10.C1V4, SM.lmRatio.model10.C1V5))
SV.lmRatio.model10.CVLevels<-do.call("rbind", list(SV.lmRatio.model10.C1V1,SV.lmRatio.model10.C1V2,SV.lmRatio.model10.C1V3,SV.lmRatio.model10.C1V4, SV.lmRatio.model10.C1V5))
# summarize for plotting
SM.lmRatio.model10CV.p<-data_summary(SM.lmRatio.model10.CVLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10CV.p<-data_summary(SV.lmRatio.model10.CVLevels, varname="value", groupnames=c("Level", "variable"))
SM.lmRatio.model10CV.p2<-data_summary2(SM.lmRatio.model10.CVLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10CV.p2<-data_summary2(SV.lmRatio.model10.CVLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatio.model10CV.p, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.01)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.01))+
geom_point(position=position_dodge(.01))+
xlab("Sequencing Variance")+
ylab("Median lmRatio (Mean +/- sd)")+
theme_classic()
## Warning: position_dodge requires non-overlapping x intervals
ggplot(SV.lmRatio.model10CV.p, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.01)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.01))+
geom_point(position=position_dodge(.01))+
xlab("Sequencing Variance")+
ylab("Variance lmRatio (Mean +/- sd)")+
theme_classic()
ggplot(SM.lmRatio.model10CV.p2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.01)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.01))+
geom_point(position=position_dodge(.01))+
xlab("Sequencing Variance")+
ylab("Median lmRatio (Median +/- min/max)")+
theme_classic()
## Warning: position_dodge requires non-overlapping x intervals
ggplot(SV.lmRatio.model10CV.p2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.01)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.01))+
geom_point(position=position_dodge(.01))+
xlab("Sequencing Variance")+
ylab("Variance lmRatio (Median +/- min/max)")+
theme_classic()
summary(aov(SM.lmRatio.model10.C1V1$value~SM.lmRatio.model10.C1V1$Level*SM.lmRatio.model10.C1V1$variable))
## Df Sum Sq Mean Sq F value Pr(>F)
## SM.lmRatio.model10.C1V1$variable 6 0.0002424 4.040e-05 1.503 0.192
## Residuals 63 0.0016933 2.688e-05
TukeyHSD(aov(SM.lmRatio.model10.C1V1$value~SM.lmRatio.model10.C1V1$Level*SM.lmRatio.model10.C1V1$variable))
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SM.lmRatio.model10.C1V1$value ~ SM.lmRatio.model10.C1V1$Level * SM.lmRatio.model10.C1V1$variable)
##
## $`SM.lmRatio.model10.C1V1$variable`
## diff lwr upr p adj
## QSeq0.5-raw -5.393265e-03 -0.012454510 0.001667980 0.2481258
## QSeq1-raw -8.387205e-04 -0.007899966 0.006222525 0.9998085
## QSeq2-raw 1.110223e-16 -0.007061245 0.007061245 1.0000000
## QSeq3-raw 0.000000e+00 -0.007061245 0.007061245 1.0000000
## QSeq10-raw 0.000000e+00 -0.007061245 0.007061245 1.0000000
## QSeq100-raw 0.000000e+00 -0.007061245 0.007061245 1.0000000
## QSeq1-QSeq0.5 4.554544e-03 -0.002506701 0.011615790 0.4470462
## QSeq2-QSeq0.5 5.393265e-03 -0.001667980 0.012454510 0.2481258
## QSeq3-QSeq0.5 5.393265e-03 -0.001667980 0.012454510 0.2481258
## QSeq10-QSeq0.5 5.393265e-03 -0.001667980 0.012454510 0.2481258
## QSeq100-QSeq0.5 5.393265e-03 -0.001667980 0.012454510 0.2481258
## QSeq2-QSeq1 8.387205e-04 -0.006222525 0.007899966 0.9998085
## QSeq3-QSeq1 8.387205e-04 -0.006222525 0.007899966 0.9998085
## QSeq10-QSeq1 8.387205e-04 -0.006222525 0.007899966 0.9998085
## QSeq100-QSeq1 8.387205e-04 -0.006222525 0.007899966 0.9998085
## QSeq3-QSeq2 -1.110223e-16 -0.007061245 0.007061245 1.0000000
## QSeq10-QSeq2 -1.110223e-16 -0.007061245 0.007061245 1.0000000
## QSeq100-QSeq2 -1.110223e-16 -0.007061245 0.007061245 1.0000000
## QSeq10-QSeq3 0.000000e+00 -0.007061245 0.007061245 1.0000000
## QSeq100-QSeq3 0.000000e+00 -0.007061245 0.007061245 1.0000000
## QSeq100-QSeq10 0.000000e+00 -0.007061245 0.007061245 1.0000000
summary(aov(SV.lmRatio.model10.C1V1$value~SV.lmRatio.model10.C1V1$Level*SV.lmRatio.model10.C1V1$variable))
## Df Sum Sq Mean Sq F value Pr(>F)
## SV.lmRatio.model10.C1V1$variable 6 0.04486 0.007476 5.711 8.65e-05 ***
## Residuals 63 0.08248 0.001309
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SV.lmRatio.model10.C1V1$value~SV.lmRatio.model10.C1V1$Level*SV.lmRatio.model10.C1V1$variable))
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SV.lmRatio.model10.C1V1$value ~ SV.lmRatio.model10.C1V1$Level * SV.lmRatio.model10.C1V1$variable)
##
## $`SV.lmRatio.model10.C1V1$variable`
## diff lwr upr p adj
## QSeq0.5-raw 4.579161e-02 -0.003489414 0.095072638 0.0852710
## QSeq1-raw 5.920835e-04 -0.048688942 0.049873109 1.0000000
## QSeq2-raw -2.146596e-02 -0.070746987 0.027815065 0.8368936
## QSeq3-raw -2.482717e-02 -0.074108198 0.024453854 0.7232841
## QSeq10-raw -3.026851e-02 -0.079549535 0.019012516 0.5069458
## QSeq100-raw -3.028966e-02 -0.079570687 0.018991365 0.5060983
## QSeq1-QSeq0.5 -4.519953e-02 -0.094480554 0.004081498 0.0929588
## QSeq2-QSeq0.5 -6.725757e-02 -0.116538598 -0.017976546 0.0018336
## QSeq3-QSeq0.5 -7.061878e-02 -0.119899810 -0.021337758 0.0009115
## QSeq10-QSeq0.5 -7.606012e-02 -0.125341147 -0.026779095 0.0002823
## QSeq100-QSeq0.5 -7.608127e-02 -0.125362299 -0.026800247 0.0002810
## QSeq2-QSeq1 -2.205804e-02 -0.071339070 0.027222982 0.8188536
## QSeq3-QSeq1 -2.541926e-02 -0.074700282 0.023861770 0.7009083
## QSeq10-QSeq1 -3.086059e-02 -0.080141619 0.018420433 0.4833416
## QSeq100-QSeq1 -3.088174e-02 -0.080162770 0.018399282 0.4825034
## QSeq3-QSeq2 -3.361211e-03 -0.052642237 0.045919814 0.9999927
## QSeq10-QSeq2 -8.802549e-03 -0.058083575 0.040478477 0.9980239
## QSeq100-QSeq2 -8.823700e-03 -0.058104726 0.040457326 0.9979972
## QSeq10-QSeq3 -5.441337e-03 -0.054722363 0.043839689 0.9998749
## QSeq100-QSeq3 -5.462489e-03 -0.054743515 0.043818537 0.9998720
## QSeq100-QSeq10 -2.115137e-05 -0.049302177 0.049259875 1.0000000
#sequence variants lm model ####
SM.lmRatio.model10.MC1V1<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1V1,method2))
SV.lmRatio.model10.MC1V1<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1V1,method2))
SM.lmRatio.model10.MC1V2<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1V2,method2))
SV.lmRatio.model10.MC1V2<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1V2,method2))
SM.lmRatio.model10.MC1V3<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1V3,method2))
SV.lmRatio.model10.MC1V3<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1V3,method2))
SM.lmRatio.model10.MC1V4<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1V4,method2))
SV.lmRatio.model10.MC1V4<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1V4,method2))
SM.lmRatio.model10.MC1V5<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1V5,method2))
SV.lmRatio.model10.MC1V5<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1V5,method2))
# prepare data for merging datasets
SM.lmRatio.model10.MC1V1$Level<-c(rep(0.1,10))
SV.lmRatio.model10.MC1V1$Level<-c(rep(0.1,10))
SM.lmRatio.model10.MC1V2$Level<-c(rep(0.2,10))
SV.lmRatio.model10.MC1V2$Level<-c(rep(0.2,10))
SM.lmRatio.model10.MC1V3$Level<-c(rep(0.5,10))
SV.lmRatio.model10.MC1V3$Level<-c(rep(0.5,10))
SM.lmRatio.model10.MC1V4$Level<-c(rep(1,10))
SV.lmRatio.model10.MC1V4$Level<-c(rep(1,10))
SM.lmRatio.model10.MC1V5$Level<-c(rep(2,10))
SV.lmRatio.model10.MC1V5$Level<-c(rep(2,10))
SM.lmRatio.model10.MC1V1<-melt(SM.lmRatio.model10.MC1V1, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.MC1V1<-melt(SV.lmRatio.model10.MC1V1, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.MC1V2<-melt(SM.lmRatio.model10.MC1V2, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.MC1V2<-melt(SV.lmRatio.model10.MC1V2, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.MC1V3<-melt(SM.lmRatio.model10.MC1V3, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.MC1V3<-melt(SV.lmRatio.model10.MC1V3, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.MC1V4<-melt(SM.lmRatio.model10.MC1V4, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.MC1V4<-melt(SV.lmRatio.model10.MC1V4, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.MC1V5<-melt(SM.lmRatio.model10.MC1V5, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.MC1V5<-melt(SV.lmRatio.model10.MC1V5, id.vars = "Level", measure.vars = method2)
# merge datasets
SM.lmRatio.model10.MCVLevels<-do.call("rbind", list(SM.lmRatio.model10.MC1V1,SM.lmRatio.model10.MC1V2,SM.lmRatio.model10.MC1V3,SM.lmRatio.model10.MC1V4, SM.lmRatio.model10.MC1V5))
SV.lmRatio.model10.MCVLevels<-do.call("rbind", list(SV.lmRatio.model10.MC1V1,SV.lmRatio.model10.MC1V2,SV.lmRatio.model10.MC1V3,SV.lmRatio.model10.MC1V4, SV.lmRatio.model10.MC1V5))
# summarize for plotting
SM.lmRatio.model10MCV.p<-data_summary(SM.lmRatio.model10.MCVLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10MCV.p<-data_summary(SV.lmRatio.model10.MCVLevels, varname="value", groupnames=c("Level", "variable"))
SM.lmRatio.model10MCV.p2<-data_summary2(SM.lmRatio.model10.MCVLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10MCV.p2<-data_summary2(SV.lmRatio.model10.MCVLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatio.model10MCV.p, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.01)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.01))+
geom_point(position=position_dodge(.01))+
xlab("Sequencing Variance")+
ylab("Median lmRatio (Mean +/- sd)")+
theme_classic()
## Warning: position_dodge requires non-overlapping x intervals
ggplot(SV.lmRatio.model10MCV.p, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.01)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.01))+
geom_point(position=position_dodge(.01))+
xlab("Sequencing Variance")+
ylab("Variance lmRatio (Mean +/- sd)")+
theme_classic()
ggplot(SM.lmRatio.model10MCV.p2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.01)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.01))+
geom_point(position=position_dodge(.01))+
xlab("Sequencing Variance")+
ylab("Median lmRatio (Median +/- min/max)")+
theme_classic()
## Warning: position_dodge requires non-overlapping x intervals
ggplot(SV.lmRatio.model10MCV.p2, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.01)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(.01))+
geom_point(position=position_dodge(.01))+
xlab("Sequencing Variance")+
ylab("Variance lmRatio (Median +/- min/max)")+
theme_classic()
summary(aov(SM.lmRatio.model10.MC1V1$value~SM.lmRatio.model10.MC1V1$Level*SM.lmRatio.model10.MC1V1$variable))
## Df Sum Sq Mean Sq F value Pr(>F)
## SM.lmRatio.model10.MC1V1$variable 6 1.816e-07 3.026e-08 1 0.433
## Residuals 63 1.906e-06 3.026e-08
TukeyHSD(aov(SM.lmRatio.model10.MC1V1$value~SM.lmRatio.model10.C1V1$Level*SM.lmRatio.model10.MC1V1$variable))
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SM.lmRatio.model10.MC1V1$value ~ SM.lmRatio.model10.C1V1$Level * SM.lmRatio.model10.MC1V1$variable)
##
## $`SM.lmRatio.model10.MC1V1$variable`
## diff lwr upr p adj
## QSeq0.5-raw -1.455364e-04 -3.824615e-04 9.138875e-05 0.5068085
## QSeq1-raw -1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq2-raw 0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq3-raw 0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq10-raw 0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq100-raw -1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq1-QSeq0.5 1.455364e-04 -9.138875e-05 3.824615e-04 0.5068085
## QSeq2-QSeq0.5 1.455364e-04 -9.138875e-05 3.824615e-04 0.5068085
## QSeq3-QSeq0.5 1.455364e-04 -9.138875e-05 3.824615e-04 0.5068085
## QSeq10-QSeq0.5 1.455364e-04 -9.138875e-05 3.824615e-04 0.5068085
## QSeq100-QSeq0.5 1.455364e-04 -9.138875e-05 3.824615e-04 0.5068085
## QSeq2-QSeq1 1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq3-QSeq1 1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq10-QSeq1 1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq100-QSeq1 0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq3-QSeq2 0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq10-QSeq2 0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq100-QSeq2 -1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq10-QSeq3 0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq100-QSeq3 -1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq100-QSeq10 -1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
summary(aov(SV.lmRatio.model10.MC1V1$value~SV.lmRatio.model10.MC1V1$Level*SV.lmRatio.model10.MC1V1$variable))
## Df Sum Sq Mean Sq F value Pr(>F)
## SV.lmRatio.model10.MC1V1$variable 6 0.06343 0.010572 14.55 2.45e-10 ***
## Residuals 63 0.04578 0.000727
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(SV.lmRatio.model10.MC1V1$value~SV.lmRatio.model10.MC1V1$Level*SV.lmRatio.model10.MC1V1$variable))
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = SV.lmRatio.model10.MC1V1$value ~ SV.lmRatio.model10.MC1V1$Level * SV.lmRatio.model10.MC1V1$variable)
##
## $`SV.lmRatio.model10.MC1V1$variable`
## diff lwr upr p adj
## QSeq0.5-raw 3.763425e-02 0.0009176365 0.074350857 0.0410116
## QSeq1-raw -1.404508e-02 -0.0507616953 0.022671526 0.9044641
## QSeq2-raw -4.013111e-02 -0.0768477220 -0.003414501 0.0233542
## QSeq3-raw -4.348794e-02 -0.0802045477 -0.006771327 0.0104158
## QSeq10-raw -4.890954e-02 -0.0856261517 -0.012192931 0.0025441
## QSeq100-raw -4.897293e-02 -0.0856895437 -0.012256323 0.0025008
## QSeq1-QSeq0.5 -5.167933e-02 -0.0883959423 -0.014962721 0.0011861
## QSeq2-QSeq0.5 -7.776536e-02 -0.1144819690 -0.041048748 0.0000004
## QSeq3-QSeq0.5 -8.112218e-02 -0.1178387947 -0.044405574 0.0000001
## QSeq10-QSeq0.5 -8.654379e-02 -0.1232603987 -0.049827178 0.0000000
## QSeq100-QSeq0.5 -8.660718e-02 -0.1233237907 -0.049890570 0.0000000
## QSeq2-QSeq1 -2.608603e-02 -0.0628026372 0.010630584 0.3296626
## QSeq3-QSeq1 -2.944285e-02 -0.0661594628 0.007273758 0.1987363
## QSeq10-QSeq1 -3.486446e-02 -0.0715810669 0.001852154 0.0734536
## QSeq100-QSeq1 -3.492785e-02 -0.0716444589 0.001788762 0.0725184
## QSeq3-QSeq2 -3.356826e-03 -0.0400734361 0.033359785 0.9999587
## QSeq10-QSeq2 -8.778430e-03 -0.0454950402 0.027938181 0.9903017
## QSeq100-QSeq2 -8.841822e-03 -0.0455584321 0.027874789 0.9899258
## QSeq10-QSeq3 -5.421604e-03 -0.0421382145 0.031295006 0.9993273
## QSeq100-QSeq3 -5.484996e-03 -0.0422016065 0.031231614 0.9992811
## QSeq100-QSeq10 -6.339196e-05 -0.0367800024 0.036653219 1.0000000
Taxon correlation outputs:
# sequencing variants taxcor ####
TaxRatio.model10.C1V1<-getTaxCor.Tab(model10.C1V1,method2)
TaxRatio.model10.C1V2<-getTaxCor.Tab(model10.C1V2,method2)
TaxRatio.model10.C1V3<-getTaxCor.Tab(model10.C1V3,method2)
TaxRatio.model10.C1V4<-getTaxCor.Tab(model10.C1V4,method2)
TaxRatio.model10.C1V5<-getTaxCor.Tab(model10.C1V5,method2)
V.TaxRatio.model10.C1V1<-melt(TaxRatio.model10.C1V1$V.tax)
M.TaxRatio.model10.C1V1<-melt(TaxRatio.model10.C1V1$Median.tax)
V.TaxRatio.model10.C1V2<-melt(TaxRatio.model10.C1V2$V.tax)
M.TaxRatio.model10.C1V2<-melt(TaxRatio.model10.C1V2$Median.tax)
V.TaxRatio.model10.C1V3<-melt(TaxRatio.model10.C1V3$V.tax)
M.TaxRatio.model10.C1V3<-melt(TaxRatio.model10.C1V3$Median.tax)
V.TaxRatio.model10.C1V4<-melt(TaxRatio.model10.C1V4$V.tax)
M.TaxRatio.model10.C1V4<-melt(TaxRatio.model10.C1V4$Median.tax)
V.TaxRatio.model10.C1V5<-melt(TaxRatio.model10.C1V5$V.tax)
M.TaxRatio.model10.C1V5<-melt(TaxRatio.model10.C1V5$Median.tax)
V.TaxRatio.model10.C1V1<-as.data.frame(V.TaxRatio.model10.C1V1)
M.TaxRatio.model10.C1V1<-as.data.frame(M.TaxRatio.model10.C1V1)
V.TaxRatio.model10.C1V2<-as.data.frame(V.TaxRatio.model10.C1V2)
M.TaxRatio.model10.C1V2<-as.data.frame(M.TaxRatio.model10.C1V2)
V.TaxRatio.model10.C1V3<-as.data.frame(V.TaxRatio.model10.C1V3)
M.TaxRatio.model10.C1V3<-as.data.frame(M.TaxRatio.model10.C1V3)
V.TaxRatio.model10.C1V4<-as.data.frame(V.TaxRatio.model10.C1V4)
M.TaxRatio.model10.C1V4<-as.data.frame(M.TaxRatio.model10.C1V4)
V.TaxRatio.model10.C1V5<-as.data.frame(V.TaxRatio.model10.C1V5)
M.TaxRatio.model10.C1V5<-as.data.frame(M.TaxRatio.model10.C1V5)
# prepare data for merging datasets
V.TaxRatio.model10.C1V1$Level<-c(rep(0.1,nrow(V.TaxRatio.model10.C1V1)))
V.TaxRatio.model10.C1V2$Level<-c(rep(0.2,nrow(V.TaxRatio.model10.C1V2)))
V.TaxRatio.model10.C1V3$Level<-c(rep(0.5,nrow(V.TaxRatio.model10.C1V3)))
V.TaxRatio.model10.C1V4$Level<-c(rep(1,nrow(V.TaxRatio.model10.C1V4)))
V.TaxRatio.model10.C1V5$Level<-c(rep(2,nrow(V.TaxRatio.model10.C1V5)))
M.TaxRatio.model10.C1V1$Level<-c(rep(0.1,nrow(M.TaxRatio.model10.C1V1)))
M.TaxRatio.model10.C1V2$Level<-c(rep(0.2,nrow(M.TaxRatio.model10.C1V2)))
M.TaxRatio.model10.C1V3$Level<-c(rep(0.5,nrow(M.TaxRatio.model10.C1V3)))
M.TaxRatio.model10.C1V4$Level<-c(rep(1,nrow(M.TaxRatio.model10.C1V4)))
M.TaxRatio.model10.C1V5$Level<-c(rep(2,nrow(M.TaxRatio.model10.C1V5)))
# merge datasets
V.TaxRatio.model10VLevels<-do.call("rbind", list(V.TaxRatio.model10.C1V1,V.TaxRatio.model10.C1V2,V.TaxRatio.model10.C1V3,V.TaxRatio.model10.C1V4,V.TaxRatio.model10.C1V5))
M.TaxRatio.model10VLevels<-do.call("rbind", list(M.TaxRatio.model10.C1V1,M.TaxRatio.model10.C1V2,M.TaxRatio.model10.C1V3,M.TaxRatio.model10.C1V4, M.TaxRatio.model10.C1V5))
# summarize for plotting
V.TaxRatio.model10.SeqV.p<-data_summary(V.TaxRatio.model10VLevels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.SeqV.p<-data_summary(M.TaxRatio.model10VLevels, varname="value", groupnames=c("Level", "Var2"))
# plot
V.TaxRatio.model10.SeqV.p2<-data_summary2(V.TaxRatio.model10VLevels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.SeqV.p2<-data_summary2(M.TaxRatio.model10VLevels, varname="value", groupnames=c("Level", "Var2"))
# plot
ggplot(V.TaxRatio.model10.SeqV.p, aes(x=Level, y=value, group = Var2, color=Var2))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(0.1))+
geom_point(position=position_dodge(0.1))+
xlab("Sequencing Depth")+
ylab("log10 Variance taxRatio (Mean +/- sd)")+
theme_classic()
## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus
## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus
## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus
## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus
## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus
## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus
## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus
ggplot(M.TaxRatio.model10.SeqV.p, aes(x=Level, y=value, group = Var2, color=Var2))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(0.1))+
geom_point(position=position_dodge(0.1))+
xlab("Sequencing Depth")+
ylab("Median taxRatio (Mean +/- sd)")+
theme_classic()
ggplot(V.TaxRatio.model10.SeqV.p2, aes(x=Level, y=value, group = Var2, color=Var2))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(0.1)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(0.1))+
geom_point(position=position_dodge(0.1))+
xlab("Sequencing Depth")+
ylab("log10 Variance taxRatio (Median +/- min/max)")+
theme_classic()
ggplot(M.TaxRatio.model10.SeqV.p2, aes(x=Level, y=value, group = Var2, color=Var2))+
geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(0.1)) +
scale_color_viridis_d(direction=-1)+
geom_line(position=position_dodge(0.1))+
geom_point(position=position_dodge(0.1))+
xlab("Sequencing Depth")+
ylab("Median taxRatio (Median +/- min/max)")+
theme_classic()
summary(aov(V.TaxRatio.model10VLevels$value~V.TaxRatio.model10VLevels$Level*V.TaxRatio.model10VLevels$Var2))
## Df Sum Sq
## V.TaxRatio.model10VLevels$Level 1 8.117e+69
## V.TaxRatio.model10VLevels$Var2 6 2.040e+69
## V.TaxRatio.model10VLevels$Level:V.TaxRatio.model10VLevels$Var2 6 1.842e+69
## Residuals 336 5.304e+71
## Mean Sq
## V.TaxRatio.model10VLevels$Level 8.117e+69
## V.TaxRatio.model10VLevels$Var2 3.400e+68
## V.TaxRatio.model10VLevels$Level:V.TaxRatio.model10VLevels$Var2 3.070e+68
## Residuals 1.579e+69
## F value Pr(>F)
## V.TaxRatio.model10VLevels$Level 5.141 0.024 *
## V.TaxRatio.model10VLevels$Var2 0.215 0.972
## V.TaxRatio.model10VLevels$Level:V.TaxRatio.model10VLevels$Var2 0.194 0.978
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(V.TaxRatio.model10VLevels$value~V.TaxRatio.model10VLevels$Level*V.TaxRatio.model10VLevels$Var2))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10VLevels$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10VLevels$Level, V.TaxRatio.model10VLevels$Var2
## Warning in TukeyHSD.aov(aov(V.TaxRatio.model10VLevels$value ~
## V.TaxRatio.model10VLevels$Level * : 'which' specified some non-factors which
## will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = V.TaxRatio.model10VLevels$value ~ V.TaxRatio.model10VLevels$Level * V.TaxRatio.model10VLevels$Var2)
##
## $`V.TaxRatio.model10VLevels$Var2`
## diff lwr upr p adj
## QSeq0.5-raw -1.337561e+33 -2.490917e+34 2.223405e+34 0.9999981
## QSeq1-raw -7.886313e+33 -3.145792e+34 1.568530e+34 0.9554309
## QSeq2-raw -3.509279e+33 -2.708089e+34 2.006233e+34 0.9994324
## QSeq3-raw -5.210814e+33 -2.878242e+34 1.836080e+34 0.9947651
## QSeq10-raw -4.570373e+33 -2.814198e+34 1.900124e+34 0.9974613
## QSeq100-raw -4.798541e+33 -2.837015e+34 1.877307e+34 0.9966721
## QSeq1-QSeq0.5 -6.548752e+33 -3.012036e+34 1.702286e+34 0.9823619
## QSeq2-QSeq0.5 -2.171719e+33 -2.574333e+34 2.139989e+34 0.9999655
## QSeq3-QSeq0.5 -3.873253e+33 -2.744486e+34 1.969836e+34 0.9990016
## QSeq10-QSeq0.5 -3.232813e+33 -2.680442e+34 2.033880e+34 0.9996464
## QSeq100-QSeq0.5 -3.460980e+33 -2.703259e+34 2.011063e+34 0.9994759
## QSeq2-QSeq1 4.377034e+33 -1.919458e+34 2.794864e+34 0.9980067
## QSeq3-QSeq1 2.675499e+33 -2.089611e+34 2.624711e+34 0.9998825
## QSeq10-QSeq1 3.315939e+33 -2.025567e+34 2.688755e+34 0.9995905
## QSeq100-QSeq1 3.087772e+33 -2.048384e+34 2.665938e+34 0.9997290
## QSeq3-QSeq2 -1.701535e+33 -2.527315e+34 2.187008e+34 0.9999919
## QSeq10-QSeq2 -1.061094e+33 -2.463270e+34 2.251052e+34 0.9999995
## QSeq100-QSeq2 -1.289261e+33 -2.486087e+34 2.228235e+34 0.9999984
## QSeq10-QSeq3 6.404407e+32 -2.293117e+34 2.421205e+34 1.0000000
## QSeq100-QSeq3 4.122734e+32 -2.315934e+34 2.398388e+34 1.0000000
## QSeq100-QSeq10 -2.281673e+32 -2.379978e+34 2.334344e+34 1.0000000
summary(aov(M.TaxRatio.model10VLevels$value~M.TaxRatio.model10VLevels$Level*M.TaxRatio.model10VLevels$Var2))
## Df Sum Sq
## M.TaxRatio.model10VLevels$Level 1 1.280e+30
## M.TaxRatio.model10VLevels$Var2 6 1.033e+29
## M.TaxRatio.model10VLevels$Level:M.TaxRatio.model10VLevels$Var2 6 9.327e+28
## Residuals 336 7.314e+31
## Mean Sq
## M.TaxRatio.model10VLevels$Level 1.280e+30
## M.TaxRatio.model10VLevels$Var2 1.722e+28
## M.TaxRatio.model10VLevels$Level:M.TaxRatio.model10VLevels$Var2 1.555e+28
## Residuals 2.177e+29
## F value Pr(>F)
## M.TaxRatio.model10VLevels$Level 5.880 0.0158 *
## M.TaxRatio.model10VLevels$Var2 0.079 0.9981
## M.TaxRatio.model10VLevels$Level:M.TaxRatio.model10VLevels$Var2 0.071 0.9986
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(M.TaxRatio.model10VLevels$value~M.TaxRatio.model10VLevels$Var2))
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = M.TaxRatio.model10VLevels$value ~ M.TaxRatio.model10VLevels$Var2)
##
## $`M.TaxRatio.model10VLevels$Var2`
## diff lwr upr p adj
## QSeq0.5-raw -6.802342e+12 -2.832820e+14 2.696773e+14 1.0000000
## QSeq1-raw -5.721834e+13 -3.336980e+14 2.192613e+14 0.9963584
## QSeq2-raw -1.927249e+13 -2.957522e+14 2.572072e+14 0.9999934
## QSeq3-raw -3.092550e+13 -3.074052e+14 2.455542e+14 0.9998923
## QSeq10-raw -2.627937e+13 -3.027590e+14 2.502003e+14 0.9999586
## QSeq100-raw -2.789322e+13 -3.043729e+14 2.485864e+14 0.9999412
## QSeq1-QSeq0.5 -5.041599e+13 -3.268957e+14 2.260637e+14 0.9982018
## QSeq2-QSeq0.5 -1.247015e+13 -2.889498e+14 2.640095e+14 0.9999995
## QSeq3-QSeq0.5 -2.412315e+13 -3.006028e+14 2.523565e+14 0.9999750
## QSeq10-QSeq0.5 -1.947703e+13 -2.959567e+14 2.570026e+14 0.9999930
## QSeq100-QSeq0.5 -2.109088e+13 -2.975706e+14 2.553888e+14 0.9999887
## QSeq2-QSeq1 3.794585e+13 -2.385338e+14 3.144255e+14 0.9996453
## QSeq3-QSeq1 2.629284e+13 -2.501868e+14 3.027725e+14 0.9999585
## QSeq10-QSeq1 3.093896e+13 -2.455407e+14 3.074186e+14 0.9998920
## QSeq100-QSeq1 2.932511e+13 -2.471546e+14 3.058048e+14 0.9999211
## QSeq3-QSeq2 -1.165301e+13 -2.881327e+14 2.648267e+14 0.9999997
## QSeq10-QSeq2 -7.006886e+12 -2.834866e+14 2.694728e+14 1.0000000
## QSeq100-QSeq2 -8.620735e+12 -2.851004e+14 2.678589e+14 0.9999999
## QSeq10-QSeq3 4.646122e+12 -2.718335e+14 2.811258e+14 1.0000000
## QSeq100-QSeq3 3.032274e+12 -2.734474e+14 2.795119e+14 1.0000000
## QSeq100-QSeq10 -1.613848e+12 -2.780935e+14 2.748658e+14 1.0000000
PERMANOVA outputs:
# sequencing variants PERMANOVA ####
model10C1V1.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1,method2, "CategoryRratio"))
model10C1V1.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1, method2, "F1Rratio"))
model10C1V1.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1, method2, "F2Rratio"))
model10C1V1.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1, method2, "F3Rratio"))
model10C1V1.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1, method2, "F4Rratio"))
model10C1V1.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1,method2, "F5Rratio"))
model10C1V2.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "CategoryRratio"))
model10C1V2.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "F1Rratio"))
model10C1V2.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "F2Rratio"))
model10C1V2.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "F3Rratio"))
model10C1V2.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "F4Rratio"))
model10C1V2.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "F5Rratio"))
model10C1V3.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "CategoryRratio"))
model10C1V3.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "F1Rratio"))
model10C1V3.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "F2Rratio"))
model10C1V3.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "F3Rratio"))
model10C1V3.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "F4Rratio"))
model10C1V3.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "F5Rratio"))
model10C1V4.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "CategoryRratio"))
model10C1V4.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "F1Rratio"))
model10C1V4.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "F2Rratio"))
model10C1V4.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "F3Rratio"))
model10C1V4.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "F4Rratio"))
model10C1V4.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "F5Rratio"))
model10C1V5.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "CategoryRratio"))
model10C1V5.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "F1Rratio"))
model10C1V5.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "F2Rratio"))
model10C1V5.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "F3Rratio"))
model10C1V5.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "F4Rratio"))
model10C1V5.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "F5Rratio"))
model10C1V1.Permanova.model$Level<-c(rep(0.1,10))
model10C1V1.Permanova.env1$Level<-c(rep(.100,10))
model10C1V1.Permanova.env2$Level<-c(rep(.100,10))
model10C1V1.Permanova.env3$Level<-c(rep(.100,10))
model10C1V1.Permanova.env4$Level<-c(rep(.100,10))
model10C1V1.Permanova.env5$Level<-c(rep(.100,10))
model10C1V2.Permanova.model$Level<-c(rep(.200,10))
model10C1V2.Permanova.env1$Level<-c(rep(.200,10))
model10C1V2.Permanova.env2$Level<-c(rep(.200,10))
model10C1V2.Permanova.env3$Level<-c(rep(.200,10))
model10C1V2.Permanova.env4$Level<-c(rep(.200,10))
model10C1V2.Permanova.env5$Level<-c(rep(.200,10))
model10C1V3.Permanova.model$Level<-c(rep(.500,10))
model10C1V3.Permanova.env1$Level<-c(rep(.500,10))
model10C1V3.Permanova.env2$Level<-c(rep(.500,10))
model10C1V3.Permanova.env3$Level<-c(rep(.500,10))
model10C1V3.Permanova.env4$Level<-c(rep(.500,10))
model10C1V3.Permanova.env5$Level<-c(rep(.500,10))
model10C1V4.Permanova.model$Level<-c(rep(1.000,10))
model10C1V4.Permanova.env1$Level<-c(rep(1.000,10))
model10C1V4.Permanova.env2$Level<-c(rep(1.000,10))
model10C1V4.Permanova.env3$Level<-c(rep(1.000,10))
model10C1V4.Permanova.env4$Level<-c(rep(1.000,10))
model10C1V4.Permanova.env5$Level<-c(rep(1.000,10))
model10C1V5.Permanova.model$Level<-c(rep(2.000,10))
model10C1V5.Permanova.env1$Level<-c(rep(2.000,10))
model10C1V5.Permanova.env2$Level<-c(rep(2.000,10))
model10C1V5.Permanova.env3$Level<-c(rep(2.000,10))
model10C1V5.Permanova.env4$Level<-c(rep(2.000,10))
model10C1V5.Permanova.env5$Level<-c(rep(2.000,10))
permanova.model10CVLevels.model<-do.call("rbind", list(model10C1V1.Permanova.model,model10C1V2.Permanova.model,model10C1V3.Permanova.model,model10C1V4.Permanova.model,model10C1V5.Permanova.model))
permanova.model10CVLevels.env1<-do.call("rbind", list(model10C1V1.Permanova.env1,model10C1V2.Permanova.env1,model10C1V3.Permanova.env1,model10C1V4.Permanova.env1,model10C1V5.Permanova.env1))
permanova.model10CVLevels.env2<-do.call("rbind", list(model10C1V1.Permanova.env2,model10C1V2.Permanova.env2,model10C1V3.Permanova.env2,model10C1V4.Permanova.env2,model10C1V5.Permanova.env2))
permanova.model10CVLevels.env3<-do.call("rbind", list(model10C1V1.Permanova.env3,model10C1V2.Permanova.env3,model10C1V3.Permanova.env3,model10C1V4.Permanova.env3,model10C1V5.Permanova.env3))
permanova.model10CVLevels.env4<-do.call("rbind", list(model10C1V1.Permanova.env4,model10C1V2.Permanova.env4,model10C1V3.Permanova.env4,model10C1V4.Permanova.env4,model10C1V5.Permanova.env4))
permanova.model10CVLevels.env5<-do.call("rbind", list(model10C1V1.Permanova.env5,model10C1V2.Permanova.env5,model10C1V3.Permanova.env5,model10C1V4.Permanova.env5,model10C1V5.Permanova.env5))
permanova.model10CVLevels.model<-melt(permanova.model10CVLevels.model, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.env1<-melt(permanova.model10CVLevels.env1, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.env2<-melt(permanova.model10CVLevels.env2, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.env3<-melt(permanova.model10CVLevels.env3, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.env4<-melt(permanova.model10CVLevels.env4, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.env5<-melt(permanova.model10CVLevels.env5, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.modelP<-data_summary(permanova.model10CVLevels.model, varname="value", groupnames=c("Level", "variable"))
permanova.model10CVLevels.env1P<-data_summary(permanova.model10CVLevels.env1, varname="value", groupnames=c("Level", "variable"))
permanova.model10CVLevels.env2P<-data_summary(permanova.model10CVLevels.env2, varname="value", groupnames=c("Level", "variable"))
permanova.model10CVLevels.env3P<-data_summary(permanova.model10CVLevels.env3, varname="value", groupnames=c("Level", "variable"))
permanova.model10CVLevels.env4P<-data_summary(permanova.model10CVLevels.env4, varname="value", groupnames=c("Level", "variable"))
permanova.model10CVLevels.env5P<-data_summary(permanova.model10CVLevels.env5, varname="value", groupnames=c("Level", "variable"))
ggplot(permanova.model10CVLevels.modelP, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.01)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(0.01))+
geom_point(position=position_dodge(0.01))+
xlab("Relative Variance (variance / mean)")+
ylab("Permanova modelRatio (Mean +/- sd)")+
theme_classic()
ggplot(permanova.model10CVLevels.env1P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(0.1))+
geom_point(position=position_dodge(0.1))+
xlab("Relative Variance (variance / mean)")+
ylab("Permanova env1Ratio (Mean +/- sd)")+
theme_classic()
ggplot(permanova.model10CVLevels.env2P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(0.1))+
geom_point(position=position_dodge(0.1))+
xlab("Relative Variance (variance / mean)")+
ylab("Permanova env2Ratio (Mean +/- sd)")+
theme_classic()
ggplot(permanova.model10CVLevels.env3P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(0.1))+
geom_point(position=position_dodge(0.1))+
xlab("Relative Variance (variance / mean)")+
ylab("Permanova env3Ratio (Mean +/- sd)")+
theme_classic()
ggplot(permanova.model10CVLevels.env4P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(0.1))+
geom_point(position=position_dodge(0.1))+
xlab("Relative Variance (variance / mean)")+
ylab("Permanova env4Ratio (Mean +/- sd)")+
theme_classic()
ggplot(permanova.model10CVLevels.env5P, aes(x=Level, y=value, group = variable, color=variable))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
scale_colour_viridis_d(direction=-1)+
geom_line(position=position_dodge(0.1))+
geom_point(position=position_dodge(0.1))+
xlab("Relative Variance (variance / mean)")+
ylab("Permanova env5Ratio (Mean +/- sd)")+
theme_classic()
summary(aov(permanova.model10CVLevels.model$value~permanova.model10CVLevels.model$Level*permanova.model10CVLevels.model$variable))
## Df
## permanova.model10CVLevels.model$Level 1
## permanova.model10CVLevels.model$variable 6
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CVLevels.model$Level 0.01517
## permanova.model10CVLevels.model$variable 0.00003
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable 0.00000
## Residuals 0.03802
## Mean Sq
## permanova.model10CVLevels.model$Level 0.015165
## permanova.model10CVLevels.model$variable 0.000004
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable 0.000000
## Residuals 0.000113
## F value
## permanova.model10CVLevels.model$Level 134.017
## permanova.model10CVLevels.model$variable 0.039
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable 0.002
## Residuals
## Pr(>F)
## permanova.model10CVLevels.model$Level <2e-16
## permanova.model10CVLevels.model$variable 1
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable 1
## Residuals
##
## permanova.model10CVLevels.model$Level ***
## permanova.model10CVLevels.model$variable
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CVLevels.model$value~permanova.model10CVLevels.model$Level*permanova.model10CVLevels.model$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.model$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.model$Level, permanova.model10CVLevels.model$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.model$value ~
## permanova.model10CVLevels.model$Level * : 'which' specified some non-factors
## which will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CVLevels.model$value ~ permanova.model10CVLevels.model$Level * permanova.model10CVLevels.model$variable)
##
## $`permanova.model10CVLevels.model$variable`
## diff lwr upr p adj
## QSeq0.5-raw -7.976089e-04 -0.007108458 0.005513241 0.9997799
## QSeq1-raw -3.568511e-05 -0.006346535 0.006275164 1.0000000
## QSeq2-raw -4.356960e-08 -0.006310893 0.006310806 1.0000000
## QSeq3-raw -1.223197e-05 -0.006323081 0.006298617 1.0000000
## QSeq10-raw 2.607455e-06 -0.006308242 0.006313457 1.0000000
## QSeq100-raw 0.000000e+00 -0.006310849 0.006310849 1.0000000
## QSeq1-QSeq0.5 7.619238e-04 -0.005548926 0.007072773 0.9998314
## QSeq2-QSeq0.5 7.975653e-04 -0.005513284 0.007108415 0.9997800
## QSeq3-QSeq0.5 7.853769e-04 -0.005525473 0.007096226 0.9997989
## QSeq10-QSeq0.5 8.002163e-04 -0.005510633 0.007111066 0.9997757
## QSeq100-QSeq0.5 7.976089e-04 -0.005513241 0.007108458 0.9997799
## QSeq2-QSeq1 3.564154e-05 -0.006275208 0.006346491 1.0000000
## QSeq3-QSeq1 2.345315e-05 -0.006287396 0.006334303 1.0000000
## QSeq10-QSeq1 3.829257e-05 -0.006272557 0.006349142 1.0000000
## QSeq100-QSeq1 3.568511e-05 -0.006275164 0.006346535 1.0000000
## QSeq3-QSeq2 -1.218840e-05 -0.006323038 0.006298661 1.0000000
## QSeq10-QSeq2 2.651025e-06 -0.006308198 0.006313500 1.0000000
## QSeq100-QSeq2 4.356960e-08 -0.006310806 0.006310893 1.0000000
## QSeq10-QSeq3 1.483942e-05 -0.006296010 0.006325689 1.0000000
## QSeq100-QSeq3 1.223197e-05 -0.006298617 0.006323081 1.0000000
## QSeq100-QSeq10 -2.607455e-06 -0.006313457 0.006308242 1.0000000
summary(aov(permanova.model10CVLevels.env1$value~permanova.model10CVLevels.env1$Level*permanova.model10CVLevels.env1$variable))
## Df
## permanova.model10CVLevels.env1$Level 1
## permanova.model10CVLevels.env1$variable 6
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CVLevels.env1$Level 0.1694
## permanova.model10CVLevels.env1$variable 0.3480
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable 0.4818
## Residuals 1.0218
## Mean Sq
## permanova.model10CVLevels.env1$Level 0.16943
## permanova.model10CVLevels.env1$variable 0.05800
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable 0.08030
## Residuals 0.00304
## F value
## permanova.model10CVLevels.env1$Level 55.71
## permanova.model10CVLevels.env1$variable 19.07
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable 26.40
## Residuals
## Pr(>F)
## permanova.model10CVLevels.env1$Level 7.26e-13
## permanova.model10CVLevels.env1$variable < 2e-16
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable < 2e-16
## Residuals
##
## permanova.model10CVLevels.env1$Level ***
## permanova.model10CVLevels.env1$variable ***
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CVLevels.env1$value~permanova.model10CVLevels.env1$Level*permanova.model10CVLevels.env1$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env1$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env1$Level, permanova.model10CVLevels.env1$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.env1$value ~
## permanova.model10CVLevels.env1$Level * : 'which' specified some non-factors
## which will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CVLevels.env1$value ~ permanova.model10CVLevels.env1$Level * permanova.model10CVLevels.env1$variable)
##
## $`permanova.model10CVLevels.env1$variable`
## diff lwr upr p adj
## QSeq0.5-raw 8.880173e-02 0.05608512 0.12151833 0.0000000
## QSeq1-raw 9.095665e-02 0.05824004 0.12367325 0.0000000
## QSeq2-raw 9.011607e-02 0.05739947 0.12283268 0.0000000
## QSeq3-raw 9.015091e-02 0.05743430 0.12286751 0.0000000
## QSeq10-raw 9.027340e-02 0.05755679 0.12299000 0.0000000
## QSeq100-raw 9.029021e-02 0.05757360 0.12300681 0.0000000
## QSeq1-QSeq0.5 2.154921e-03 -0.03056168 0.03487153 0.9999953
## QSeq2-QSeq0.5 1.314347e-03 -0.03140226 0.03403095 0.9999998
## QSeq3-QSeq0.5 1.349180e-03 -0.03136742 0.03406578 0.9999997
## QSeq10-QSeq0.5 1.471670e-03 -0.03124493 0.03418827 0.9999995
## QSeq100-QSeq0.5 1.488478e-03 -0.03122813 0.03420508 0.9999995
## QSeq2-QSeq1 -8.405745e-04 -0.03355718 0.03187603 1.0000000
## QSeq3-QSeq1 -8.057416e-04 -0.03352235 0.03191086 1.0000000
## QSeq10-QSeq1 -6.832510e-04 -0.03339986 0.03203335 1.0000000
## QSeq100-QSeq1 -6.664430e-04 -0.03338305 0.03205016 1.0000000
## QSeq3-QSeq2 3.483288e-05 -0.03268177 0.03275144 1.0000000
## QSeq10-QSeq2 1.573235e-04 -0.03255928 0.03287393 1.0000000
## QSeq100-QSeq2 1.741315e-04 -0.03254247 0.03289074 1.0000000
## QSeq10-QSeq3 1.224906e-04 -0.03259411 0.03283910 1.0000000
## QSeq100-QSeq3 1.392986e-04 -0.03257731 0.03285590 1.0000000
## QSeq100-QSeq10 1.680797e-05 -0.03269980 0.03273341 1.0000000
summary(aov(permanova.model10CVLevels.env2$value~permanova.model10CVLevels.env2$Level*permanova.model10CVLevels.env2$variable))
## Df
## permanova.model10CVLevels.env2$Level 1
## permanova.model10CVLevels.env2$variable 6
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CVLevels.env2$Level 0.0917
## permanova.model10CVLevels.env2$variable 1.7809
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable 0.2365
## Residuals 1.5862
## Mean Sq
## permanova.model10CVLevels.env2$Level 0.09171
## permanova.model10CVLevels.env2$variable 0.29682
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable 0.03941
## Residuals 0.00472
## F value
## permanova.model10CVLevels.env2$Level 19.427
## permanova.model10CVLevels.env2$variable 62.873
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable 8.348
## Residuals
## Pr(>F)
## permanova.model10CVLevels.env2$Level 1.41e-05
## permanova.model10CVLevels.env2$variable < 2e-16
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable 1.90e-08
## Residuals
##
## permanova.model10CVLevels.env2$Level ***
## permanova.model10CVLevels.env2$variable ***
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CVLevels.env2$value~permanova.model10CVLevels.env2$Level*permanova.model10CVLevels.env2$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env2$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env2$Level, permanova.model10CVLevels.env2$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.env2$value ~
## permanova.model10CVLevels.env2$Level * : 'which' specified some non-factors
## which will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CVLevels.env2$value ~ permanova.model10CVLevels.env2$Level * permanova.model10CVLevels.env2$variable)
##
## $`permanova.model10CVLevels.env2$variable`
## diff lwr upr p adj
## QSeq0.5-raw 2.026056e-01 0.16184313 0.24336797 0.0000000
## QSeq1-raw 2.038560e-01 0.16309363 0.24461847 0.0000000
## QSeq2-raw 2.041906e-01 0.16342815 0.24495299 0.0000000
## QSeq3-raw 2.040283e-01 0.16326583 0.24479067 0.0000000
## QSeq10-raw 2.041921e-01 0.16342968 0.24495453 0.0000000
## QSeq100-raw 2.041991e-01 0.16343667 0.24496151 0.0000000
## QSeq1-QSeq0.5 1.250498e-03 -0.03951192 0.04201292 1.0000000
## QSeq2-QSeq0.5 1.585022e-03 -0.03917740 0.04234744 0.9999998
## QSeq3-QSeq0.5 1.422700e-03 -0.03933972 0.04218512 0.9999999
## QSeq10-QSeq0.5 1.586552e-03 -0.03917587 0.04234897 0.9999998
## QSeq100-QSeq0.5 1.593538e-03 -0.03916888 0.04235596 0.9999998
## QSeq2-QSeq1 3.345237e-04 -0.04042790 0.04109695 1.0000000
## QSeq3-QSeq1 1.722021e-04 -0.04059022 0.04093462 1.0000000
## QSeq10-QSeq1 3.360543e-04 -0.04042637 0.04109848 1.0000000
## QSeq100-QSeq1 3.430403e-04 -0.04041938 0.04110546 1.0000000
## QSeq3-QSeq2 -1.623216e-04 -0.04092474 0.04060010 1.0000000
## QSeq10-QSeq2 1.530680e-06 -0.04076089 0.04076395 1.0000000
## QSeq100-QSeq2 8.516614e-06 -0.04075391 0.04077094 1.0000000
## QSeq10-QSeq3 1.638523e-04 -0.04059857 0.04092627 1.0000000
## QSeq100-QSeq3 1.708382e-04 -0.04059158 0.04093326 1.0000000
## QSeq100-QSeq10 6.985934e-06 -0.04075544 0.04076941 1.0000000
summary(aov(permanova.model10CVLevels.env3$value~permanova.model10CVLevels.env3$Level*permanova.model10CVLevels.env3$variable))
## Df
## permanova.model10CVLevels.env3$Level 1
## permanova.model10CVLevels.env3$variable 6
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CVLevels.env3$Level 0.2228
## permanova.model10CVLevels.env3$variable 1.7409
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable 0.4492
## Residuals 0.8949
## Mean Sq
## permanova.model10CVLevels.env3$Level 0.22276
## permanova.model10CVLevels.env3$variable 0.29015
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable 0.07487
## Residuals 0.00266
## F value
## permanova.model10CVLevels.env3$Level 83.63
## permanova.model10CVLevels.env3$variable 108.93
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable 28.11
## Residuals
## Pr(>F)
## permanova.model10CVLevels.env3$Level <2e-16
## permanova.model10CVLevels.env3$variable <2e-16
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable <2e-16
## Residuals
##
## permanova.model10CVLevels.env3$Level ***
## permanova.model10CVLevels.env3$variable ***
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CVLevels.env3$value~permanova.model10CVLevels.env3$Level*permanova.model10CVLevels.env3$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env3$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env3$Level, permanova.model10CVLevels.env3$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.env3$value ~
## permanova.model10CVLevels.env3$Level * : 'which' specified some non-factors
## which will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CVLevels.env3$value ~ permanova.model10CVLevels.env3$Level * permanova.model10CVLevels.env3$variable)
##
## $`permanova.model10CVLevels.env3$variable`
## diff lwr upr p adj
## QSeq0.5-raw 2.007164e-01 0.17009861 0.23133426 0.0000000
## QSeq1-raw 2.015977e-01 0.17097990 0.23221554 0.0000000
## QSeq2-raw 2.019095e-01 0.17129167 0.23252732 0.0000000
## QSeq3-raw 2.016198e-01 0.17100197 0.23223762 0.0000000
## QSeq10-raw 2.017276e-01 0.17110981 0.23234545 0.0000000
## QSeq100-raw 2.016901e-01 0.17107231 0.23230795 0.0000000
## QSeq1-QSeq0.5 8.812880e-04 -0.02973654 0.03149911 1.0000000
## QSeq2-QSeq0.5 1.193061e-03 -0.02942476 0.03181088 0.9999998
## QSeq3-QSeq0.5 9.033652e-04 -0.02971446 0.03152119 1.0000000
## QSeq10-QSeq0.5 1.011197e-03 -0.02960663 0.03162902 0.9999999
## QSeq100-QSeq0.5 9.736974e-04 -0.02964413 0.03159152 0.9999999
## QSeq2-QSeq1 3.117726e-04 -0.03030605 0.03092960 1.0000000
## QSeq3-QSeq1 2.207723e-05 -0.03059575 0.03063990 1.0000000
## QSeq10-QSeq1 1.299086e-04 -0.03048791 0.03074773 1.0000000
## QSeq100-QSeq1 9.240946e-05 -0.03052541 0.03071023 1.0000000
## QSeq3-QSeq2 -2.896954e-04 -0.03090752 0.03032813 1.0000000
## QSeq10-QSeq2 -1.818641e-04 -0.03079969 0.03043596 1.0000000
## QSeq100-QSeq2 -2.193632e-04 -0.03083719 0.03039846 1.0000000
## QSeq10-QSeq3 1.078313e-04 -0.03050999 0.03072565 1.0000000
## QSeq100-QSeq3 7.033223e-05 -0.03054749 0.03068816 1.0000000
## QSeq100-QSeq10 -3.749910e-05 -0.03065532 0.03058032 1.0000000
summary(aov(permanova.model10CVLevels.env4$value~permanova.model10CVLevels.env4$Level*permanova.model10CVLevels.env4$variable))
## Df
## permanova.model10CVLevels.env4$Level 1
## permanova.model10CVLevels.env4$variable 6
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CVLevels.env4$Level 0.003
## permanova.model10CVLevels.env4$variable 0.259
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable 0.006
## Residuals 4.262
## Mean Sq
## permanova.model10CVLevels.env4$Level 0.00328
## permanova.model10CVLevels.env4$variable 0.04320
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable 0.00105
## Residuals 0.01268
## F value
## permanova.model10CVLevels.env4$Level 0.259
## permanova.model10CVLevels.env4$variable 3.406
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable 0.083
## Residuals
## Pr(>F)
## permanova.model10CVLevels.env4$Level 0.61146
## permanova.model10CVLevels.env4$variable 0.00282
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable 0.99785
## Residuals
##
## permanova.model10CVLevels.env4$Level
## permanova.model10CVLevels.env4$variable **
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CVLevels.env4$value~permanova.model10CVLevels.env4$Level*permanova.model10CVLevels.env4$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env4$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env4$Level, permanova.model10CVLevels.env4$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.env4$value ~
## permanova.model10CVLevels.env4$Level * : 'which' specified some non-factors
## which will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CVLevels.env4$value ~ permanova.model10CVLevels.env4$Level * permanova.model10CVLevels.env4$variable)
##
## $`permanova.model10CVLevels.env4$variable`
## diff lwr upr p adj
## QSeq0.5-raw 7.992923e-02 0.01311574 0.14674273 0.0079832
## QSeq1-raw 7.737040e-02 0.01055690 0.14418389 0.0117590
## QSeq2-raw 7.681439e-02 0.01000089 0.14362788 0.0127681
## QSeq3-raw 7.735739e-02 0.01054390 0.14417089 0.0117817
## QSeq10-raw 7.742544e-02 0.01061195 0.14423894 0.0116631
## QSeq100-raw 7.743403e-02 0.01062054 0.14424753 0.0116482
## QSeq1-QSeq0.5 -2.558835e-03 -0.06937233 0.06425466 0.9999998
## QSeq2-QSeq0.5 -3.114845e-03 -0.06992834 0.06369865 0.9999994
## QSeq3-QSeq0.5 -2.571840e-03 -0.06938533 0.06424166 0.9999998
## QSeq10-QSeq0.5 -2.503787e-03 -0.06931728 0.06430971 0.9999998
## QSeq100-QSeq0.5 -2.495198e-03 -0.06930869 0.06431830 0.9999998
## QSeq2-QSeq1 -5.560095e-04 -0.06736950 0.06625749 1.0000000
## QSeq3-QSeq1 -1.300446e-05 -0.06682650 0.06680049 1.0000000
## QSeq10-QSeq1 5.504873e-05 -0.06675845 0.06686854 1.0000000
## QSeq100-QSeq1 6.363769e-05 -0.06674986 0.06687713 1.0000000
## QSeq3-QSeq2 5.430050e-04 -0.06627049 0.06735650 1.0000000
## QSeq10-QSeq2 6.110582e-04 -0.06620244 0.06742455 1.0000000
## QSeq100-QSeq2 6.196471e-04 -0.06619385 0.06743314 1.0000000
## QSeq10-QSeq3 6.805319e-05 -0.06674544 0.06688155 1.0000000
## QSeq100-QSeq3 7.664215e-05 -0.06673685 0.06689014 1.0000000
## QSeq100-QSeq10 8.588960e-06 -0.06680491 0.06682208 1.0000000
summary(aov(permanova.model10CVLevels.env5$value~permanova.model10CVLevels.env5$Level*permanova.model10CVLevels.env5$variable))
## Df
## permanova.model10CVLevels.env5$Level 1
## permanova.model10CVLevels.env5$variable 6
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable 6
## Residuals 336
## Sum Sq
## permanova.model10CVLevels.env5$Level 0.211
## permanova.model10CVLevels.env5$variable 0.781
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable 0.544
## Residuals 7.748
## Mean Sq
## permanova.model10CVLevels.env5$Level 0.21103
## permanova.model10CVLevels.env5$variable 0.13009
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable 0.09065
## Residuals 0.02306
## F value
## permanova.model10CVLevels.env5$Level 9.152
## permanova.model10CVLevels.env5$variable 5.642
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable 3.931
## Residuals
## Pr(>F)
## permanova.model10CVLevels.env5$Level 0.00268
## permanova.model10CVLevels.env5$variable 1.34e-05
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable 0.00082
## Residuals
##
## permanova.model10CVLevels.env5$Level **
## permanova.model10CVLevels.env5$variable ***
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable ***
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(aov(permanova.model10CVLevels.env5$value~permanova.model10CVLevels.env5$Level*permanova.model10CVLevels.env5$variable))
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env5$Level
## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env5$Level, permanova.model10CVLevels.env5$variable
## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.env5$value ~
## permanova.model10CVLevels.env5$Level * : 'which' specified some non-factors
## which will be dropped
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = permanova.model10CVLevels.env5$value ~ permanova.model10CVLevels.env5$Level * permanova.model10CVLevels.env5$variable)
##
## $`permanova.model10CVLevels.env5$variable`
## diff lwr upr p adj
## QSeq0.5-raw 1.349313e-01 0.04484332 0.22501925 0.0002421
## QSeq1-raw 1.352374e-01 0.04514948 0.22532541 0.0002317
## QSeq2-raw 1.343638e-01 0.04427584 0.22445178 0.0002624
## QSeq3-raw 1.353955e-01 0.04530749 0.22548342 0.0002266
## QSeq10-raw 1.349400e-01 0.04485204 0.22502797 0.0002418
## QSeq100-raw 1.348424e-01 0.04475439 0.22493032 0.0002452
## QSeq1-QSeq0.5 3.061568e-04 -0.08978181 0.09039412 1.0000000
## QSeq2-QSeq0.5 -5.674746e-04 -0.09065544 0.08952049 1.0000000
## QSeq3-QSeq0.5 4.641732e-04 -0.08962379 0.09055214 1.0000000
## QSeq10-QSeq0.5 8.719429e-06 -0.09007925 0.09009669 1.0000000
## QSeq100-QSeq0.5 -8.893162e-05 -0.09017690 0.08999903 1.0000000
## QSeq2-QSeq1 -8.736314e-04 -0.09096160 0.08921433 1.0000000
## QSeq3-QSeq1 1.580164e-04 -0.08992995 0.09024598 1.0000000
## QSeq10-QSeq1 -2.974374e-04 -0.09038540 0.08979053 1.0000000
## QSeq100-QSeq1 -3.950884e-04 -0.09048305 0.08969288 1.0000000
## QSeq3-QSeq2 1.031648e-03 -0.08905632 0.09111961 1.0000000
## QSeq10-QSeq2 5.761940e-04 -0.08951177 0.09066416 1.0000000
## QSeq100-QSeq2 4.785430e-04 -0.08960942 0.09056651 1.0000000
## QSeq10-QSeq3 -4.554538e-04 -0.09054342 0.08963251 1.0000000
## QSeq100-QSeq3 -5.531048e-04 -0.09064107 0.08953486 1.0000000
## QSeq100-QSeq10 -9.765105e-05 -0.09018562 0.08999032 1.0000000
leveneTest(permanova.model10CVLevels.model$value~permanova.model10CVLevels.model$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 0.0147 1
## 343
leveneTest(permanova.model10CVLevels.env1$value~permanova.model10CVLevels.env1$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 41.537 < 2.2e-16 ***
## 343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10CVLevels.env2$value~permanova.model10CVLevels.env2$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 56.935 < 2.2e-16 ***
## 343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10CVLevels.env3$value~permanova.model10CVLevels.env3$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 95.357 < 2.2e-16 ***
## 343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10CVLevels.env4$value~permanova.model10CVLevels.env4$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 32.326 < 2.2e-16 ***
## 343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(permanova.model10CVLevels.env5$value~permanova.model10CVLevels.env5$variable)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 6 18.764 < 2.2e-16 ***
## 343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Conclusions:
Performance of all methods is highest at low sparcity, high sampling depth, and low sampling variance.
Model.Microbiome provides an empirical framework for optimizing sequence count normalization methods prior to making ecological inferences; in our example the parameters for QSeq0.5 resulted in a consistent underperformance compared to other parameters.
Model.Microbiome constructs networks and network plots using two heuristics for creating the network thresholds. It also includes some functions to simplify accessing the network statistics that have been calculated, and plots that are generated. These are illustrated in the example below. These networks are built using two alternative approaches. Whenever we build a network, we need to establish a threshold to determine what relationships we consider significant to include. Our two methods include one that is a static threshold value, set at a correlation coefficient of 0.8; the other is a dynamic threshold heuristic that identifies the maximum threshold value that results in a network with 250 edges. The reason we include the secon method is because the network statistics for two graphs with different number of edges are in principle not comparable. However, we have found that in ecological settings that while the metrics we use might change, the overall interpretation of each plot does not. We also find that similar to other measures of beta diversity (here interpreted as changing species associations across sites), that statistics derived from the network are sensitive to network construction method, but are robust to normalization methods of the community. Let’s take a look an an example using the community structure example from earlier in the tutorial:
method3<-c("model", "raw", "QSeq0.5", "QSeq10")
plotstats.A<-getNetStats(model10.A, method3) # get statistics
## [1] 4
## [1] 0.410976
## [1] 0.358304
## [1] 0.3624654
## [1] 0.358304
## [1] 0.3843079
## [1] 0.3998413
## [1] 0.4045508
## [1] 0.3998413
## [1] 0.3866272
## [1] 0.4247437
## [1] 0.4294848
## [1] 0.4247437
## [1] 0.2361243
## [1] 0.2167414
## [1] 0.2167414
## [1] 0.2167414
## [1] 0.4499039
## [1] 0.4329779
## [1] 0.4579468
## [1] 0.4329779
## [1] 0.461248
## [1] 0.477312
## [1] 0.471168
## [1] 0.477312
## [1] 0.2728415
## [1] 0.1432485
## [1] 0.1702268
## [1] 0.1407465
## [1] 0.248736
## [1] 0.2950365
## [1] 0.289536
## [1] 0.2950365
## [1] 0.2729277
## [1] 0.243103
## [1] 0.245344
## [1] 0.243103
## [1] 0.5104065
## [1] 0.5656
## [1] 0.5603943
## [1] 0.5656
plotstats.A$D.module.table # modularity value table for dynamic threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.4109760 0.3583040 0.3624654 0.3583040
## rep 2 0.3843079 0.3998413 0.4045508 0.3998413
## rep 3 0.3866272 0.4247437 0.4294848 0.4247437
## rep 4 0.2361243 0.2167414 0.2167414 0.2167414
## rep 5 0.4499039 0.4329779 0.4579468 0.4329779
## rep 6 0.4612480 0.4773120 0.4711680 0.4773120
## rep 7 0.2728415 0.1432485 0.1702268 0.1407465
## rep 8 0.2487360 0.2950365 0.2895360 0.2950365
## rep 9 0.2729277 0.2431030 0.2453440 0.2431030
## rep 10 0.5104065 0.5656000 0.5603943 0.5656000
plotstats.A$S.module.table # modularity value table for static threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.09944751 0.10169492 0.10000000 0.10169492
## rep 2 0.04097614 0.03657802 0.03512783 0.03657802
## rep 3 0.09493751 0.10342449 0.10342449 0.10342449
## rep 4 0.02987515 0.03089773 0.02550441 0.03089773
## rep 5 0.13171200 0.13817258 0.13714286 0.13817258
## rep 6 0.26509864 0.27045830 0.27191176 0.27045830
## rep 7 0.00000000 0.00000000 0.00000000 0.00000000
## rep 8 0.32680079 0.35605760 0.35605760 0.35605760
## rep 9 0.10811033 0.10957908 0.11389167 0.10957908
## rep 10 0.06818182 0.07692308 0.07692308 0.07692308
A close look at the module table suggests that the characteristics of the un-noralized dataset are driving the network statistics of the normalized set. For example, if we look at rep1, the values for QSeq0.5 and QSeq10 are both close or identical to the values for the raw dataset. This means that this normalization technique is not necessarily improving the accuracy of the network statistics. We can see this pattern does not depend on whether the network is constructed using a dynamic or static threshold. We can look at the threshold cutoff for the dynamic network construction to see if there are any patterns:
plotstats.A$D.Threshold.table # table of threshold values for dynamic threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.955 0.944 0.943 0.944
## rep 2 0.982 0.980 0.980 0.980
## rep 3 0.978 0.975 0.975 0.975
## rep 4 0.988 0.987 0.987 0.987
## rep 5 0.970 0.962 0.962 0.962
## rep 6 0.932 0.929 0.929 0.929
## rep 7 0.998 0.997 0.997 0.997
## rep 8 0.731 0.712 0.714 0.712
## rep 9 0.972 0.966 0.966 0.966
## rep 10 0.982 0.977 0.976 0.977
As before the QSeq methods do not provide an improvement over the raw dataset. We can use this method to look at differences in internal structure. The pattern is the same:
plotstats.B<-getNetStats(model10.B, method3) # get statistics
## [1] 4
## [1] 0.4771983
## [1] 0.437088
## [1] 0.4297682
## [1] 0.437088
## [1] 0.643872
## [1] 0.643872
## [1] 0.643872
## [1] 0.643872
## [1] 0.353504
## [1] 0.324192
## [1] 0.324192
## [1] 0.324192
## [1] 0.260736
## [1] 0.2855883
## [1] 0.2917726
## [1] 0.2855883
## [1] 0.268128
## [1] 0.293312
## [1] 0.293312
## [1] 0.293312
## [1] 0.3045163
## [1] 0.300704
## [1] 0.300704
## [1] 0.300704
## [1] 0.311319
## [1] 0.354592
## [1] 0.3487969
## [1] 0.354592
## [1] 0.333184
## [1] 0.349888
## [1] 0.349888
## [1] 0.349888
## [1] 0.317536
## [1] 0.280896
## [1] 0.280896
## [1] 0.280896
## [1] 0.488352
## [1] 0.497184
## [1] 0.497184
## [1] 0.497184
plotstats.B$D.module.table # modularity value table for dynamic threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.4771983 0.4370880 0.4297682 0.4370880
## rep 2 0.6438720 0.6438720 0.6438720 0.6438720
## rep 3 0.3535040 0.3241920 0.3241920 0.3241920
## rep 4 0.2607360 0.2855883 0.2917726 0.2855883
## rep 5 0.2681280 0.2933120 0.2933120 0.2933120
## rep 6 0.3045163 0.3007040 0.3007040 0.3007040
## rep 7 0.3113190 0.3545920 0.3487969 0.3545920
## rep 8 0.3331840 0.3498880 0.3498880 0.3498880
## rep 9 0.3175360 0.2808960 0.2808960 0.2808960
## rep 10 0.4883520 0.4971840 0.4971840 0.4971840
plotstats.B$D.Threshold.table # table of threshold values for dynamic threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.953 0.949 0.949 0.949
## rep 2 0.414 0.392 0.382 0.392
## rep 3 0.893 0.892 0.892 0.892
## rep 4 0.977 0.967 0.967 0.967
## rep 5 0.802 0.799 0.800 0.799
## rep 6 0.924 0.921 0.921 0.920
## rep 7 0.963 0.962 0.961 0.962
## rep 8 0.894 0.897 0.892 0.897
## rep 9 0.929 0.941 0.937 0.941
## rep 10 0.081 0.083 0.084 0.084
plotstats.B$S.module.table # modularity value table for static threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.11114921 0.12333215 0.12505602 0.12333215
## rep 2 0.74710648 0.74133333 0.73440000 0.74133333
## rep 3 0.12431002 0.14444288 0.14296729 0.14444288
## rep 4 0.04015084 0.05331283 0.05331283 0.05331283
## rep 5 0.26812800 0.29331200 0.29331200 0.29331200
## rep 6 0.17940219 0.17437673 0.17376731 0.17437673
## rep 7 0.24861363 0.24861363 0.24861363 0.24861363
## rep 8 0.32632674 0.32453978 0.32632674 0.32453978
## rep 9 0.30511937 0.31266437 0.31266437 0.30887663
## rep 10 0.78710744 0.78826531 0.79316713 0.78826531
plotstats.B$S.Threshold.table # table of threshold values for static threshold (0.8)
## model raw QSeq0.5 QSeq10
## rep 1 0.8 0.8 0.8 0.8
## rep 2 0.8 0.8 0.8 0.8
## rep 3 0.8 0.8 0.8 0.8
## rep 4 0.8 0.8 0.8 0.8
## rep 5 0.8 0.8 0.8 0.8
## rep 6 0.8 0.8 0.8 0.8
## rep 7 0.8 0.8 0.8 0.8
## rep 8 0.8 0.8 0.8 0.8
## rep 9 0.8 0.8 0.8 0.8
## rep 10 0.8 0.8 0.8 0.8
plotstats.C<-getNetStats(model10.C, method3) # get statistics
## [1] 4
## [1] 0.439264
## [1] 0.439264
## [1] 0.439264
## [1] 0.433327
## [1] 0.369088
## [1] 0.39248
## [1] 0.39248
## [1] 0.39248
## [1] 0.531808
## [1] 0.529248
## [1] 0.533152
## [1] 0.529248
## [1] 0.5050391
## [1] 0.4929453
## [1] 0.486236
## [1] 0.4929453
## [1] 0.422784
## [1] 0.42864
## [1] 0.4032
## [1] 0.42864
## [1] 0.393487
## [1] 0.3870622
## [1] 0.3870622
## [1] 0.3870622
## [1] 0.492
## [1] 0.4745528
## [1] 0.475776
## [1] 0.481184
## [1] 0.4798279
## [1] 0.4735569
## [1] 0.46755
## [1] 0.4735569
## [1] 0.467456
## [1] 0.43392
## [1] 0.43392
## [1] 0.43392
## [1] 0.392256
## [1] 0.3770156
## [1] 0.381012
## [1] 0.3770156
plotstats.C$D.module.table # modularity value table for dynamic threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.4392640 0.4392640 0.4392640 0.4333270
## rep 2 0.3690880 0.3924800 0.3924800 0.3924800
## rep 3 0.5318080 0.5292480 0.5331520 0.5292480
## rep 4 0.5050391 0.4929453 0.4862360 0.4929453
## rep 5 0.4227840 0.4286400 0.4032000 0.4286400
## rep 6 0.3934870 0.3870622 0.3870622 0.3870622
## rep 7 0.4920000 0.4745528 0.4757760 0.4811840
## rep 8 0.4798279 0.4735569 0.4675500 0.4735569
## rep 9 0.4674560 0.4339200 0.4339200 0.4339200
## rep 10 0.3922560 0.3770156 0.3810120 0.3770156
plotstats.C$D.Threshold.table # table of threshold values for dynamic threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.160 0.160 1.570000e-01 0.159
## rep 2 0.730 0.717 7.170000e-01 0.717
## rep 3 0.074 0.078 8.300000e-02 0.078
## rep 4 0.039 0.039 3.800000e-02 0.039
## rep 5 0.607 0.651 6.440000e-01 0.651
## rep 6 0.142 0.151 1.510000e-01 0.151
## rep 7 0.066 0.082 8.200000e-02 0.083
## rep 8 0.001 0.004 3.000000e-03 0.004
## rep 9 0.809 0.801 8.000000e-01 0.801
## rep 10 0.001 0.001 -8.812395e-16 0.001
plotstats.C$S.module.table # modularity value table for static threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.7957064 0.8040816 0.8040816 0.8040816
## rep 2 0.4786784 0.4952257 0.4952257 0.4952257
## rep 3 0.8510742 0.8616667 0.8616667 0.8616667
## rep 4 0.7958478 0.7865014 0.7865014 0.7865014
## rep 5 0.6811435 0.6722044 0.6765062 0.6722044
## rep 6 0.8126722 0.8028571 0.8028571 0.8028571
## rep 7 0.8144290 0.8144290 0.8144290 0.8144290
## rep 8 0.7566163 0.7474074 0.7474074 0.7474074
## rep 9 0.4533535 0.4322339 0.4391534 0.4322339
## rep 10 0.9149660 0.9152893 0.9251701 0.9152893
plotstats.C$S.Threshold.table # table of threshold values for static threshold (0.8)
## model raw QSeq0.5 QSeq10
## rep 1 0.8 0.8 0.8 0.8
## rep 2 0.8 0.8 0.8 0.8
## rep 3 0.8 0.8 0.8 0.8
## rep 4 0.8 0.8 0.8 0.8
## rep 5 0.8 0.8 0.8 0.8
## rep 6 0.8 0.8 0.8 0.8
## rep 7 0.8 0.8 0.8 0.8
## rep 8 0.8 0.8 0.8 0.8
## rep 9 0.8 0.8 0.8 0.8
## rep 10 0.8 0.8 0.8 0.8
plotstats.D<-getNetStats(model10.D, method3) # get statistics
## [1] 4
## [1] 0.340544
## [1] 0.343392
## [1] 0.343392
## [1] 0.343392
## [1] 0.5121567
## [1] 0.519968
## [1] 0.524224
## [1] 0.519968
## [1] 0.441568
## [1] 0.449408
## [1] 0.448224
## [1] 0.449408
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0.324288
## [1] 0.344608
## [1] 0.349792
## [1] 0.344608
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0.490848
## [1] 0.475386
## [1] 0.467104
## [1] 0.475386
## [1] 0.321568
## [1] 0.304128
## [1] 0.304128
## [1] 0.304128
## [1] 0.486912
## [1] 0.490784
## [1] 0.490784
## [1] 0.490784
## [1] 0
## [1] 0
## [1] 0
## [1] 0
plotstats.D$D.module.table # modularity value table for dynamic threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.3405440 0.343392 0.343392 0.343392
## rep 2 0.5121567 0.519968 0.524224 0.519968
## rep 3 0.4415680 0.449408 0.448224 0.449408
## rep 4 0.0000000 0.000000 0.000000 0.000000
## rep 5 0.3242880 0.344608 0.349792 0.344608
## rep 6 0.0000000 0.000000 0.000000 0.000000
## rep 7 0.4908480 0.475386 0.467104 0.475386
## rep 8 0.3215680 0.304128 0.304128 0.304128
## rep 9 0.4869120 0.490784 0.490784 0.490784
## rep 10 0.0000000 0.000000 0.000000 0.000000
plotstats.D$D.Threshold.table # table of threshold values for dynamic threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.681 0.680 0.681 0.680
## rep 2 0.125 0.108 0.121 0.109
## rep 3 0.089 0.092 0.090 0.092
## rep 4 -0.001 -0.001 -0.001 -0.001
## rep 5 0.675 0.657 0.656 0.657
## rep 6 -0.001 -0.001 -0.001 -0.001
## rep 7 0.004 0.004 0.007 0.004
## rep 8 0.687 0.670 0.671 0.670
## rep 9 0.622 0.614 0.614 0.614
## rep 10 -0.001 -0.001 -0.001 -0.001
plotstats.D$S.module.table # modularity value table for static threshold
## model raw QSeq0.5 QSeq10
## rep 1 0.4815760 0.4912190 0.4838156 0.4912190
## rep 2 0.5682973 0.5682973 0.5682973 0.5682973
## rep 3 0.8097826 0.8097826 0.8034568 0.8097826
## rep 4 0.7992304 0.7903646 0.7903646 0.7903646
## rep 5 0.6353308 0.6320232 0.6358643 0.6320232
## rep 6 0.7210884 0.7210884 0.7210884 0.7210884
## rep 7 0.8008163 0.7919550 0.7919550 0.7919550
## rep 8 0.5468444 0.5562307 0.5682404 0.5562307
## rep 9 0.6132653 0.6253061 0.6253061 0.6253061
## rep 10 0.7761341 0.7761341 0.7761341 0.7761341
plotstats.D$S.Threshold.table # table of threshold values for static threshold (0.8)
## model raw QSeq0.5 QSeq10
## rep 1 0.8 0.8 0.8 0.8
## rep 2 0.8 0.8 0.8 0.8
## rep 3 0.8 0.8 0.8 0.8
## rep 4 0.8 0.8 0.8 0.8
## rep 5 0.8 0.8 0.8 0.8
## rep 6 0.8 0.8 0.8 0.8
## rep 7 0.8 0.8 0.8 0.8
## rep 8 0.8 0.8 0.8 0.8
## rep 9 0.8 0.8 0.8 0.8
## rep 10 0.8 0.8 0.8 0.8
What this tells us is that this normalization technique does not have a large influence on the overall modularity statistic for the network; it does not improve our ability to identify clusters of associating or dissociating taxa. These metrics may still be useful in the case that methods are identified that do significantly improve the accuracy of replicating the network structure from before sampling; or in identifying cases where a normalization technique significantly decreases the accuracy of replicating the network structure from before sampling.
We can also visualize the plots:
getNetPlot(model10.A[1],method3)
Some figures from the data for the paper:
In each experiment, LII
ggplot(model10Levels.summary1[model10Levels.summary1$variable == "raw"|
model10Levels.summary1$variable == "QSeq0.5"|
model10Levels.summary1$variable == "QSeq2"|
model10Levels.summary1$variable == "QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.2, position=position_dodge(.3), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(.3), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(.3), size=1)+
xlab("Degree of Structure")+
ylab("LII Value (Mean +/- standard dev)")+
theme_classic()
#model10.SeqLevels.summary2
ggplot(model10.SeqLevels.summary[model10.SeqLevels.summary$variable == "raw"|model10.SeqLevels.summary$variable == "QSeq0.5"|model10.SeqLevels.summary$variable == "QSeq2"|model10.SeqLevels.summary$variable == "QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=100, position=position_dodge(70), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(70), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(70), size=1)+
xlab("Sampling Depth")+
ylab("LII Value (Mean +/- standard dev)")+
theme_classic()
ggplot(model10.SeqVarLevels.summary[model10.SeqVarLevels.summary$variable == "raw"|
model10.SeqVarLevels.summary$variable == "QSeq0.5"|
model10.SeqVarLevels.summary$variable == "QSeq2"|
model10.SeqVarLevels.summary$variable == "QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(.08), size=1)+
xlab("Relative Variance (variance / mean)")+
ylab("LII Value (Mean +/- standard dev)")+
theme_classic()
# Figure 3: rank abundance curve
par(mfrow=c(2,2))
barplot(sort(taxa_sums(model10.A$rep1$model$comm)/1000000, TRUE),
las = 2, main ="Rank Abundance Lowest Sparcity", ylab="Million Counts")
barplot(sort(taxa_sums(model10.B$rep1$model$comm)/1000000, TRUE),
las = 2, main ="Rank Abundance Low Sparcity", ylab="Million Counts")
barplot(sort(taxa_sums(model10.C$rep1$model$comm)/1000000, TRUE),
las = 2, main ="Rank Abundance High Sparcity", ylab="Million Counts")
barplot(sort(taxa_sums(model10.D$rep1$model$comm)/1000000, TRUE),
las = 2, main ="Rank Abundance Highest Sparcity", ylab="Million Counts")
# figure 5
#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.modelP[permanova.model10CVLevels.modelP$variable=="raw" |
permanova.model10CVLevels.modelP$variable=="QSeq0.5" |
permanova.model10CVLevels.modelP$variable=="QSeq2" |
permanova.model10CVLevels.modelP$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(.08), size=1)+
xlab("Relative Variance (variance / mean)")+
ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
ggtitle("Experimental Model")+
theme_classic()
#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.env1P[permanova.model10CVLevels.env1P$variable=="raw" |
permanova.model10CVLevels.env1P$variable=="QSeq0.5" |
permanova.model10CVLevels.env1P$variable=="QSeq2" |
permanova.model10CVLevels.env1P$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(.08), size=1)+
xlab("Relative Variance (variance / mean)")+
ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
ggtitle("Environmental Factor 1")+
theme_classic()
#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.env2P[permanova.model10CVLevels.env2P$variable=="raw" |
permanova.model10CVLevels.env2P$variable=="QSeq0.5" |
permanova.model10CVLevels.env2P$variable=="QSeq2" |
permanova.model10CVLevels.env2P$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(.08), size=1)+
xlab("Relative Variance (variance / mean)")+
ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
ggtitle("Environmental Factor 2")+
theme_classic()
#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.env3P[permanova.model10CVLevels.env3P$variable=="raw" |
permanova.model10CVLevels.env3P$variable=="QSeq0.5" |
permanova.model10CVLevels.env3P$variable=="QSeq2" |
permanova.model10CVLevels.env3P$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(.08), size=1)+
xlab("Relative Variance (variance / mean)")+
ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
ggtitle("Environmental Factor 3")+
theme_classic()
#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.env4P[permanova.model10CVLevels.env4P$variable=="raw" |
permanova.model10CVLevels.env4P$variable=="QSeq0.5" |
permanova.model10CVLevels.env4P$variable=="QSeq2" |
permanova.model10CVLevels.env4P$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(.08), size=1)+
xlab("Relative Variance (variance / mean)")+
ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
ggtitle("Environmental Factor 4")+
theme_classic()
#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.env5P[permanova.model10CVLevels.env5P$variable=="raw" |
permanova.model10CVLevels.env5P$variable=="QSeq0.5" |
permanova.model10CVLevels.env5P$variable=="QSeq2" |
permanova.model10CVLevels.env5P$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(.08), size=1)+
xlab("Relative Variance (variance / mean)")+
ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
ggtitle("Environmental Factor 5")+
theme_classic()
# Figure 5
#SV.lmRatio.model10CV.p
ggplot(SV.lmRatio.model10CV.p[SV.lmRatio.model10CV.p$variable=="raw" |
SV.lmRatio.model10CV.p$variable=="QSeq0.5" |
SV.lmRatio.model10CV.p$variable=="QSeq2" |
SV.lmRatio.model10CV.p$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(.08), size=1)+
xlab("Relative Sampling Variance (variance / mean)")+
ylab("Linear Model R-Ratio Variance (Mean +/- standard dev)")+
ggtitle("Variance of Linear Model R-Ratio")+
theme_classic()
SV.lmRatio.model10MCV.p
#SV.lmRatio.model10MCV.p
ggplot(SV.lmRatio.model10MCV.p[SV.lmRatio.model10MCV.p$variable=="raw" |
SV.lmRatio.model10MCV.p$variable=="QSeq0.5" |
SV.lmRatio.model10MCV.p$variable=="QSeq2" |
SV.lmRatio.model10MCV.p$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
#scale_colour_viridis_d(direction=-1)+
scale_colour_grey()+
geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
geom_point(position=position_dodge(.08), size=1)+
xlab("Relative Sampling Variance (variance / mean)")+
ylab("Linear Model R-Ratio Variance (Mean +/- standard dev)")+
ggtitle("Variance of Linear Model R-Ratio")+
theme_classic()
#devtools::install_github("ricardo-bion/ggradar", dependencies=TRUE)
#library(ggradar)
# table of output summary
#PERMANOVA.Model
#PERMANOVA.F1
#PERMANOVA.F2
#PERMANOVA.F3
#PERMANOVA.F4
#PERMANOVA.F5
#lmRatio.model(mean)
#lmRatio.model(var)
#lmRatio.env(mean)
#lmRatio.env(var)
#taxRatio
#LII.R
#LII
#getRadar<-function(x, method){
# Summarize.LII(x, method)
#
#}
#Summarize.LII(model10.A, method2)
##Summarize.PERMANOVA.Rratio(model10.A, method2, "CategoryRratio")
#Summarize.PERMANOVA.Rratio(model10.A, method2, "F1Rratio")
#Summarize.PERMANOVA.Rratio(model10.A, method2, "F2Rratio")
#Summarize.PERMANOVA.Rratio(model10.A, method2, "F3Rratio")
#Summarize.PERMANOVA.Rratio(model10.A, method2, "F4Rratio")
#Summarize.PERMANOVA.Rratio(model10.A, method2, "F5Rratio")
#Summarize.lmRatiotabModel.Median(model10.A, method2)
#Summarize.lmRatiotabModel.Var(model10.A, method2)
#Summarize.lmRatiotab.Median(model10.A, method2)
#Summarize.lmRatiotab.Var(model10.A, method2)
#getTaxCor.Tab(model10.A, method2)
#Summarize.LII(model10.A, method2)
#dtest<-rbind(as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "CategoryRratio")), as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F1Rratio")), as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F2Rratio")), as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F3Rratio")), as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F4Rratio")), as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F5Rratio")), as.data.frame(Summarize.lmRatiotabModel.Median(model10.A, method2)), as.data.frame(Summarize.lmRatiotabModel.Var(model10.A, method2)), as.data.frame(Summarize.lmRatiotab.Median(model10.A, method2)), as.data.frame(Summarize.lmRatiotab.Var(model10.A, method2)),
# 1-as.data.frame(Summarize.LII(model10.A, method2))) #as.data.frame(getTaxCor.Tab(model10.A, method2)$V.tax),
#as.data.frame(getTaxCor.Tab(model10.A, method2)$Median.tax),
#dtest<-data.frame("cat"=c(rep("PERMANOVA.Cat", 10),
# rep("PERMANOVA.F1", 10),
# rep("PERMANOVA.F2", 10),
# rep("PERMANOVA.F3", 10),
# rep("PERMANOVA.F4", 10),
# rep("PERMANOVA.F5", 10),
# rep("lm.model.median", 10),
# rep("lm.model.var", 10),
# rep("lm.median", 10),
# rep("lm.var", 10),
# #rep("Taxcor.Var", 10),
# #rep("taxcor.median", 10),
# rep("LII", 10)),
# dtest)
#dsum<-ddply(dtest, "cat", summarise,
# raw=mean(raw),
# QSeq0.5=mean(QSeq0.5),
# QSeq1=mean(QSeq1),
# QSeq2=mean(QSeq2),
# QSeq3=mean(QSeq3),
# QSeq10=mean(QSeq10),
# QSeq100=mean(QSeq100)
# )
#library(tibble)
#dsum%>%mutate_at(vars(-cat),funs(scales::rescale))->test
#test<-as.data.frame(test)
#test<-
#ggradar(test)
#t(test)
#ds2<-melt(dtest)
#ds3<-melt(dsum)
#rownames(dsum)<-dsum$cat
#dsum<-dsum[,-1]
#library(fmsb)
#dsum<-as.data.frame(t(dsum))
#radarchart(ds2, vlcex=0.5, pcol=c("gray8", "gray35","gray48","gray65","gray70","gray87","khaki4"))
#plot(dsum)
#library(ggiraphExtra)
#ggRadar(ds3, aes(x=cat, y=value, group=cat))+facet_wrap(~variable)
We have found that sometimes in the reference there are substantive differences in the network between static and dynamic network construction; but that in subsampled data these differences are reduced. There is considerable variation in outcomes; and it raises a question of what characteristics of reference datasets lead to different outcomes when we apply the two network building methods. This is not a question we will try to answer here.
A couple post-script comments about interpreting metabarcoding output data:
It’s important to be aware of what metrics are robust to changes in methodology, and which are not. In general betadiversity is robust because the relationships of the dominant taxa have higher weight in most betadiversity metrics, and so their relationships tend to be easily captured and replicated in all analyses. However, alpha diversity is not like this. We have chosen not to address it in this software because in practice alpha diversity counts are heavily dependent on the type of sequence QC that is employed. We do not model sequence quality and do not try to address sequence QC. In general, we treat analyses that hinge on alpha diversity in microbiome studies as highly suspect because endogenous factors, like the presence of disease, will skew the taxon abundance distribution and affect the accuracy and comparability of an alpha diversity estimate. Alpha diversity estimates often rely on an assumption that either the sampling effort was the same; or that the taxon abundance distribution of one sample can be infered from other samples. So far, both of these assumptions are essentially never met. I’ll explain:
Sampling effort is not the same as sequencing depth. The principle of sampling effort is rooted in physical effort because it acts to standardize the counts by area or distance covered. This provides results that accurately represent changes in density of sampled species across sites. It is well understood that sequence data does not do this. However, there is a widely held misconception that taking the same number of sequences from a sample across the dataset (i.e. even rarefaction) does represent a standardization of sampling effort. It does not. It is the equivalent of doing a sampling of the rainforest and the temperate deciduous forest by identifying the first 100 trees we encounter. This approach would tell us nothing of the density of the respective trees; only give us information about the relative position of each tree within the species abundance distribution of each forest. To standardize sampling effort, we need an index of species abundance that actually embodies information about the abundance of the species. For example, if in this survey, we record how far we travel to encounter 100 trees, and finish our count calculation by dividing tree counts by the total distance we had to survey, then then we would have an output value that accurately tells us something about the abundance of specific species independent of the abundance of others. This is the key purpose of normalizing for sampling effort. Since we do not end up with a spatially explicit estimate of taxon abundance by using even rarefaction, it is not in principle a normalization of sampling effort. Approaches that do not infer a taxon density are difficult to reliably use for estimating alpha diveristy.
The taxon abundance distribution is often infered across samples. There are instances where this may be appropriate, however in most environmental microbiome studies it is not. Endogenous factors like the presence of a pathogen can result in a large change in the species abundance distribution at a single site. It may be possible, given ecological knowledge of specific members, to make such an assumption based on the known behavior and interactions of members of the community. But no software currently accounts for the ecological role of microbes in attempting to infer the species abundance curve of undersampled experimental units. Therefore, the current approaches to infering species abundance curves are inherently unreliable, and blind to the role that species interactions have on structuring the species abundance curve.
This is all to say: alpha diversity metrics in microbiome metabarcoding studies should be taken with a hefty grain of salt, and the analysis of these studies should probably not hinge on the alpha diversity estimates.